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.
Coordinate Geometry is one of the most high-scoring and concept-driven chapters inCOMEDK 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 detailedCOMEDK UGET 2026 Mathematics syllabusto 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 |
|
Conic Sections |
| |
Three-dimensional Geometry |
|
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 x2+ y2- 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:
x2+ y2- 6x + 2y = 0
We will complete the square for both the x and y terms:
Starting with the x terms:
x2- 6x
Add and subtract (6/2)2= 9
x2- 6x + 9 - 9 = (x - 3)2- 9
Next, for the y terms:
y2+ 2y
Add and subtract (2/2)2= 1
y2+ 2y + 1 - 1 = (y+1)2- 1
Now substitute these results back into the original equation:
x2- 6x + y2+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 - y1= m(x - x1)
Where, (x1,y1) = (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 y2= 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 y2= 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 y2= 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
x2/a2+ y2/b2= 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-b2/a2)
Substitute a = 3b into the eccentricity formula:
e = √[1-b2/(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 x2/a2- y2/b2= 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
x2/a2- y2/b2= 1
the foci are located at
± c with c2= a2+ b2
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, e2= ce/a
e2= 3/2
We also know that for this hyperbola,
e2= 1+b2/a2
Setting these equal gives:
1 + b2/a2= 3/2
Subtract 1 from both sides
b2/a2= 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!