JEE Main Parabola Practice Questions With Solutions

If the tangent at a point P on the parabola $y^2=3x$y^{2} = 3 x is parallel to the line $x+2y=1$x + 2 y = 1 and the tangents at the points Q and R on the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$\frac{x^{2}}{4} + \frac{y^{2}}{1} = 1 are perpendicular to the line $x-y=2$x - y = 2, then the area of the triangle PQR is :

The equations of two sides of a variable triangle are $x=0$x = 0 and $y=3$y = 3, and its third side is a tangent to the parabola $y^2=6x$y^{2} = 6 x. The locus of its circumcentre is :

The distance of the point $(6,-2\sqrt{2})$\left(\right. 6 , - 2 \sqrt{2} \left.\right) from the common tangent $\mathrm{y}=\mathrm{mx}+\mathrm{c},\mathrm{m}>0$y = mx + c , m > 0, of the curves $x=2y^2$x = 2 y^{2} and $x=1+y^2$x = 1 + y^{2} is :

The equations of the sides AB and AC of a triangle ABC are $(\lambda +1)x+\lambda y=4$\left(\right. \lambda + 1 \left.\right) x + \lambda y = 4 and $\lambda x+(1-\lambda )y+\lambda =0$\lambda x + \left(\right. 1 - \lambda \left.\right) y + \lambda = 0 respectively. Its vertex A is on the y-axis and its orthocentre is (1, 2). The length of the tangent from the point C to the part of the parabola $y^2=6x$y^{2} = 6 x in the first quadrant is :

Let a tangent to the curve ${\mathrm{y}}^2=24\mathrm{x}$y^{2} = 24 x meet the curve $xy=2$x y = 2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the :

Let the focal chord of the parabola $\mathrm{P}:y^2=4x$P : y^{2} = 4 x along the line $\mathrm{L}:y=\mathrm{m}x+\mathrm{c},\mathrm{m}>0$L : y = m x + c , m > 0 meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola $\mathrm{H}:x^2-y^2=4$H : x^{2} - y^{2} = 4. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :

If the tangents drawn at the points $\mathrm{P}$P and $\mathrm{Q}$Q on the parabola $y^2=2x-3$y^{2} = 2 x - 3 intersect at the point $R(0,1)$R \left(\right. 0 , 1 \left.\right), then the orthocentre of the triangle $PQR$P Q R is :

If the length of the latus rectum of a parabola, whose focus is $(a,a)$\left(\right. a , a \left.\right) and the tangent at its vertex is $x+y=a$x + y = a, is 16, then $|a|$\left|\right. a \left|\right. is equal to :

Let $P(a,b)$P \left(\right. a , b \left.\right) be a point on the parabola $y^2=8x$y^{2} = 8 x such that the tangent at $P$P passes through the centre of the circle $x^2+y^2-10x-14y+65=0$x^{2} + y^{2} - 10 x - 14 y + 65 = 0. Let $A$A be the product of all possible values of $a$a and $B$B be the product of all possible values of $b$b. Then the value of $A+B$A + B is equal to :

Let $\mathrm{P}$P and $\mathrm{Q}$Q be any points on the curves $(x-1{)}^2+(y+1{)}^2=1$\left(\right. x - 1 \left.\right)^{2} + \left(\right. y + 1 \left.\right)^{2} = 1 and $y=x^2$y = x^{2}, respectively. The distance between $P$P and $Q$Q is minimum for some value of the abscissa of $P$P in the interval :