COMEDK UGET 2026 Coordinate Geometry Practice Questions with Solutions

Based on past year's paper analysis, COMEDK UGET 2026 Coordinate Geometry practice questions with solutions have been provided here. By regularly solving COMEDK Coordinate Geometry sample questions, you can easily score solid 12-13 marks in the Math section.

Table of Contents

COMEDK UGET 2026 Coordinate Geometry Important Topics
COMEDK UGET 2026 Coordinate Geometry Expected Weightage
COMEDK UGET 2026 Coordinate Geometry Practice Questions with Solutions
Smart Study Strategy for Coordinate Geometry
Previous Year Questions from Coordinate Geometry

COMEDK UGET Coordinate Geometry Practice Questions with Solutions

Coordinate Geometry is one of the most high-scoring and concept-driven chapters in COMEDK UGET 2026 , and when you practice Coordinate Geometry questions with solutions, you strengthen both your accuracy and speed. As a student, you will notice that this chapter directly tests your understanding of graphs, equations, and geometric interpretation rather than rote formulas. The most important portions you must focus on include Straight Lines, Circle, Parabola, Ellipse, Hyperbola, Pair of Straight Lines, and Distance & Section Formula. Among these, Straight Lines and Circles consistently carry the highest weightage, while conic sections together form a significant chunk of the paper. Since COMEDK questions are typically single-step or moderate two-step problems, mastering the basics of coordinate geometry gives you a strong advantage over other aspirants.

When you analyze the type and nature of questions asked, you will find that COMEDK UGET primarily focuses on formula-based conceptual applications rather than lengthy calculations. You are often asked questions on finding the equation of a line, distance between a point and a line, radius or center of a circle, tangent and normal concepts, locus-based questions, and conditions of intersection between lines and conics. From previous year trends, questions have frequently appeared from slope and intercept form of straight lines, combined equation of pair of lines, standard equation of circle, length of tangent, and simple properties of parabola such as focus–directrix and latus rectum. Ellipse and hyperbola questions are fewer but usually direct, testing definitions and standard results rather than deep derivations.

To prepare effectively for Coordinate Geometry for COMEDK UGET 2026, you should follow a practice-oriented strategy. Start by revising all standard formulas and geometric interpretations, then immediately move to topic-wise practice questions with solved examples so that you understand the thought process behind each solution. You should solve previous year COMEDK questions first, as they clearly reflect the exam’s difficulty level and repetition pattern. While practicing, focus on diagram visualization, sign conventions, and elimination techniques, since many questions can be solved faster without full calculations. Regular timed practice and error analysis will help you avoid common traps, making Coordinate Geometry one of the most reliable scoring areas in your COMEDK UGET 2026 preparation.

Also Check - Do or Die Chapters for COMEDK UGET 2026 Mathematics

COMEDK UGET 2026 Coordinate Geometry Important Topics

The authorities have provided the detailed COMEDK UGET 2026 Mathematics syllabus to help students prepare for the upcoming exam. COMEDK Coordinate Geometry question paper covers mainly three topics: Straight Lines, Conic Sections, and Three-Dimensional Geometry. In the following table, we have listed the section-wise syllabus here:

Chapter	Section	Topics
Coordinate Geometry	Straight Lines	Brief recall of two-dimensional geometry. Slope of a line and the angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form, intercept form. Distance of a point from a line.
	Conic Sections	Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line, and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
	Three-dimensional Geometry	Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points.

COMEDK UGET 2026 Coordinate Geometry Expected Weightage

Coordinate Geometry carries some of the highest weightage, around 20%. Around 12-13questios are asked from COMEDK Coordinate Geometry sample questions. In the following table, we have detailed Coordinate Geometry expected weighatge in COMEDK UGET 2026:

Topic	Expected Number of Questions	Expected Weightage
Coordinate Geometry	12-13	20%

COMEDK UGET 2026 Coordinate Geometry Practice Questions with Solutions

COMEDK UGET 2026 Coordinate Geometry practice questions with solutions are provided below. You should solve these questions to practice for the exam in a diligent manner.

Q1. Let ABC be a triangle with equations of its sides AB, BC, CA respectively are x - 2 = 0, y - 5 = 0, and 5x + 2y - 10 = 0. Then the orthocentre of the triangle lies on the line is?

a. 4x + y = 13

b. 3x + y = 1

c. x - y = 0

d. X - 2y = 0

Ans. a. 4x + y = 13

Solution: We are given that the sides of triangle ABC are:

AB: x - 2 = 0

BC: y - 5 = 0

CA: 5x + 2y - 10 = 0

Let's break it down step by step.

Determine the vertices by finding the intersections of the lines:

Intersection of x - 2 = 0 and y - 5 = 0

x = 2, y = 5

So one vertex is B(2, 5)

Intersection of x - 2 = 0 and 5x + 2y - 10 = 0

Substitute x = 2 into 5x + 2y - 10 = 0

5(2) + 2y - 10 = 0; 2y = 0; y = 0

Thus, the corresponding vertex is A(2,0)

Intersection of y - 5 = 0 and 5x + 2y - 10 = 0

Substitute y = 5 into 5x + 2y - 10 = 0

5x + 2(5) - 10 = 0; 5x = 0; x = 0

Therefore, the third vertex is C(0,5)

Identify the right angle:

Notice that line x - 2 = 0, is vertical and line y - 5 = 0, is horizontal. These lines are perpendicular, so the angle at their intersection, point B(2,5), is 90°.

Find the orthocentre:

In a right-angled triangle, the orthocentre is located at the vertex where the right angle occurs. Since the right angle is at B(2,5), the orthocentre is also B(2,5)

Check which of the given lines passes through the orthocentre B(2,5)

Option A: 3x + y = 1

Substitute x = 2 and y = 5:

3(2) + 5 = 6 + 5 = 11 (≠ 1)

Thus, the orthocentre (2,5) lies on the line 4x + y = 13, which is option a.

Q2. The equation of a circle passing through the origin is x ² + y ² - 6x + 2y = 0. The equation of one of its diameters is:

a. 3x - y = 0

b. x + 3y = 0

c. x - 3y = 0

d. x + y = 0

Ans. b. x + 3y = 0

Solution: To determine the equation of one of the diameters of the given circle, we need to first rewrite the equation of the circle in its standard form. The given equation is:

x ² + y ² - 6x + 2y = 0

We will complete the square for both the x and y terms:

Starting with the x terms:

x ² - 6x

Add and subtract (6/2) ² = 9

x ² - 6x + 9 - 9 = (x - 3) ² - 9

Next, for the y terms:

y ² + 2y

Add and subtract (2/2) ² = 1

y ² + 2y + 1 - 1 = (y+1) ² - 1

Now substitute these results back into the original equation:

x ² - 6x + y ² +2y = 0

Becomes:

[(x-3) ² - 9] + [(y+1) ² - 1] = 0

Simplify it,

(x-3) ² + (y+1) ² - 10 = 0

This is equivalent to:

(x-3) ² + (y+1) ² = 10

This represents a circle with center at (3, -1) and radius √10

The equation of a diameter of the circle must pass through the center, (3, -1), and the origin, (0,0). We can find the equation of the line passing through these two points using the point-slope form.

The slope of the line passing through (3, -1) and (0,0) is:

Slope [0-(-1)]/0-3 = 1/-3 = -1/3

Using the point-slope form of the line equation:

y - y ₁ = m(x - x ₁ )

Where, (x ₁ ,y ₁ ) = (3,-1) and m = -1/3, we get,

y + 1 = -1/3 (x - 3)

Multiply through by 3 to clear the fraction:

3(y+1) = -(x-3)

Simplify the equation:

3y + 3 = -x + 3

Rearrange to get the standard form of the line equation:

x + 3y = 0

Therefore, the equation of one of its diameters is:

Option D.

Q3. In the parabola y ² = 4ax, the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is?

a. x + 2y = 0

b. x -2y = 0

c. 2x + y = 0

d. 2x - y = 0

Ans. c. 2x + y = 0

Solution: The length of the latus rectum of the parabola y ² = 4ax is 4a

Given that the length of the latus rectum is 6 units, we have 4a = 6. Therefore, a = 3/2

The equation of the parabola becomes y ² = 6x

The vertex of the parabola is at the origin (0,0), and the negative end of the latus rectum is at the point (-a, 2a), which is (-3/2, 3) in this case. The slope of the chord passing through the vertex and the negative end of the latus rectum is (3-0)/-3/2-0 = -2.

The equation of the chord in point-slope form is y - 0 = -2(x-0), which simplifies to y = -2x

Therefore, the equation of the chord is 2x + y = 0

Q4. If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

a. 1/√2

b. 2/√3

c. 1/√3

d. 2√2/3

Ans. 2√2/3

Solution: To find the eccentricity of the ellipse, we start with the given information that the length of the major axis of an ellipse is 3 times the length of the minor axis. First, let's define the standard notation for an ellipse and apply the given information.

The standard form of the ellipse with the major and minor axes along the x-axis and y-axis respectively is

x ² /a ² + y ² /b ² = 1.

where a is the semi-major axis and b is the semi-minor axis. The length of the major axis is 2a and the length of the minor axis is 2b. Given that the length of the major axis is 3 times the length of the minor axis, we have: 2a = 3(2b)

Or,

a = 3b

The eccentricity e of an ellipse is given by the formula:

e = √(1-b ² /a ² )

Substitute a = 3b into the eccentricity formula:

e = √[1-b ² /(3b) ² ]

Simplifying the equation,

e = √8/2

Or, e = 2√2/3

Q5. If the distance between the foci and the distance between the two directrices are in the ratio 3:2 for a hyperbola x ² /a ² - y ² /b ² = 1; then a:b is:

a. √2:1

b. 1:2

c. √3:√2

d. 2:1

Ans. a. √2:1

Solution: Let's work through the problem step-by-step.

For the hyperbola

x ² /a ² - y ² /b ² = 1

the foci are located at

± c with c ² = a ² + b ²

Thus, the distance between the foci is 2c.

The directrices of this hyperbola are given by,

x = ± a/e,

Where the eccentricity is

e = c/a.

Therefore, the distance between the two directrices is

2(a/e)

According to the problem, the ratio of the distance between the foci to the distance between the directrices is

2c/2(a/e) = ce/a = 3/2

Since the eccentricity is

e = c/a.

Multiplying by e, e ² = ce/a

e ² = 3/2

We also know that for this hyperbola,

e ² = 1+b ² /a ²

Setting these equal gives:

1 + b ² /a ² = 3/2

Subtract 1 from both sides

b ² /a ² = 3/2 - 1 = 1/2

Taking square roots on both sides, we find:

b/a = 1/√2,

which can be rewritten as

b:a = √2:1

Smart Study Strategy for Coordinate Geometry

Check the tips to cover coordinate geometry for the COMEDK exam.

Portion / Topic	Key Concepts You Must Cover	Type of Questions Asked in COMEDK	Previous Year Focus Areas	How You Should Study This Portion
Distance Formula & Section Formula	Distance between two points, internal & external division, midpoint	Direct formula-based numerical questions	Internal division ratio, midpoint-based geometry	Memorize formulas, practice 15–20 direct questions, focus on sign accuracy
Area of Triangle & Collinearity	Area using determinant, condition for collinearity	Conceptual + formula application	Collinearity check using area = 0	Practice determinant calculation, avoid arithmetic mistakes
Straight Lines – Basics	Slope, angle between lines, parallel & perpendicular conditions	Direct and conceptual	Slope conditions, angle between two lines	Master slope concepts, solve previous year questions first
Straight Lines – Equations	Point-slope, slope-intercept, two-point form	Formula-based application	Equation through given points, conversion of forms	Practice form conversion and identify fastest approach
Distance of a Point from a Line	Perpendicular distance formula	Single-step numerical	Distance from point to line	Practice direct substitution, focus on absolute value handling
Pair of Straight Lines	Combined equation, angle between pair, condition for perpendicularity	Conceptual + moderate calculation	Homogeneous equations, angle between pair	Understand coefficient comparison; practice selected PYQs
Circle – Standard Equation	Center, radius, general to standard form	Very frequently asked	Finding center/radius from equation	Practice completing squares quickly
Circle – Tangent & Normal	Length of tangent, equation of tangent	Formula-based conceptual	Length of tangent, condition of tangency	Memorize formulas, practice standard models
Circle – Intersection Concepts	Intersection of line & circle	Conceptual reasoning	Condition for touching/intersecting	Focus on discriminant-based approach
Parabola – Basics	Standard equation, focus, directrix, latus rectum	Direct conceptual	Focus–directrix based questions	Memorize properties, visualize graphs
Parabola – Tangent & Normal	Equation of tangent, parametric form	Less frequent but scoring	Tangent at given point	Practice limited but standard questions
Ellipse – Basics	Standard equation, major/minor axis, eccentricity	Direct formula-based	Eccentricity and axis length	Focus on definitions and standard values
Ellipse – Properties	Foci, latus rectum	Conceptual	Property-based MCQs	Revise formulas repeatedly; avoid derivations
Hyperbola – Basics	Standard equation, asymptotes	Direct conceptual	Equation identification	Memorize asymptote formulas
Hyperbola – Properties	Foci, eccentricity	Rare but direct	Eccentricity-based	Quick revision, limited practice
Locus Problems	Definition-based locus formation	Conceptual reasoning	Distance-based locus	Practice visualization-based problems
Graph Interpretation	Identification of conic from equation	Conceptual	Recognizing graph type	Practice converting equations to standard form

Previous Year Questions from Coordinate Geometry

Check the nature and area of questions from this topic.

Sub-topic	Portion Asked	Nature of Questions	Approx. Frequency (Last 5–6 Years)	Difficulty Level	Exam Trend
Distance Formula	Distance between two points	Direct numerical	1 question almost every year	Easy	Very formula-based, quick scoring
Section Formula	Internal division, midpoint	Direct application	1 question in alternate years	Easy	Often combined with geometry interpretation
Area of Triangle	Collinearity condition	Conceptual + formula	1 question in 2–3 years	Easy–Moderate	Tests determinant understanding
Straight Line – Slope	Finding slope, angle between lines	Conceptual	1–2 questions every year	Easy	One of the most repeated areas
Straight Line – Equation Forms	Two-point, point-slope form	Formula-based	1 question every year	Easy–Moderate	Focus on form conversion
Point–Line Distance	Perpendicular distance	Direct formula	1 question frequently	Easy	High accuracy, low time
Pair of Straight Lines	Angle between pair, condition of perpendicularity	Conceptual	1 question in most years	Moderate	Coefficient comparison important
Circle – Standard Equation	Finding center & radius	Very frequent	1–2 questions every year	Easy	One of the highest-weightage topics
Circle – General Form	Converting general to standard	Formula manipulation	1 question every year	Easy–Moderate	Completing square is essential
Length of Tangent (Circle)	Tangent from external point	Direct formula	1 question in most years	Easy	Repeated numerical pattern
Line–Circle Intersection	Condition of intersection/tangency	Conceptual	1 question in alternate years	Moderate	Uses discriminant logic
Parabola – Basics	Focus, directrix, latus rectum	Direct conceptual	1 question almost every year	Easy	Definition-based
Parabola – Equation	Standard form identification	Direct	1 question in 2 years	Easy	Graph understanding helps
Parabola – Tangent	Equation of tangent	Formula-based	Rare (once in 4–5 years)	Moderate	Usually single-step
Ellipse – Standard Equation	Major/minor axis, eccentricity	Direct	1 question in 2–3 years	Easy	Tests memory of formulas
Ellipse – Properties	Foci, latus rectum	Conceptual	Rare	Easy	Very straightforward
Hyperbola – Basics	Standard equation, asymptotes	Direct conceptual	Rare but predictable	Easy	Pure formula-based
Hyperbola – Properties	Eccentricity	Rare	Easy	Simple substitution
Locus Problems	Distance-based locus	Conceptual reasoning	1 question in some years	Moderate	Requires visualization
Graph Identification	Identifying conic from equation	Conceptual	Asked occasionally	Easy–Moderate	Convert to standard form

Coordinate Geometry covers a significant part of the Mathematics syllabus in COMEDK exam, thus making it one of the most important chapters. You should focus on important chapters from the syllabus, and solve as many COMEDK UGET 2026 Coordinate Geometry practice questions as possible. We hope this article about COMEDK UGET 2026 Coordinate Geometry Practice Questions with Solutions was helpful to you. For more such articles and information, stay tuned to CollegeDekho!