List of top Mathematics Questions on Parabola asked in JEE Main

Two tangent lines l₁ and l₂ are drawn from the point (2, 0) to the parabola 2y² = – x. If the lines l₁ and l₂ are also tangent to the circle (x – 5)² + y² = r, then 17r is equal to _________.

Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

The area of the region enclosed between the parabolas y² = 2x – 1 and y² = 4x – 3 is

Let PQ be a focal chord of the parabola y² = 4x such that it subtends an angle of π/2 at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse \(E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a^2>b^2.\) If e is the eccentricity of the ellipse E, then the value of \(\frac{1}{e^2}\) is equal to

Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :

The area (in s units) of the smaller of the two circles that touch the parabola, $y^2 = 4x$ at the point $(1, 2)$ and the x-axis is :

The length of the chord of the parabola $x^2 = 4y$ having equation $x - \sqrt{2} y + 4 \sqrt{2} = 0$ is :

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$ . If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in s units) is equal to :

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

The line $x - 2y = 2$ meets the parabola, $y^2 + 2x = 0$ only at the point $(- 2,-2)$. The line $ y=mx-\frac{1}{2m}\left(m\ne0\right)$ is tangent to the parabola, $y^{2} = - 2x$ at the point $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

If the length of focal chord of y² = 12x is 15 and if the distance of the focal chord from origin is p then 10p² is equal to:

If the normal at point P $$$(a{t}_1^2,2a{t}_1)$ and $Q$$(a{t}_2^2,2a{t}_2)$ on the parabola $y^2=4ax$ meet on the parabola, the$t_1{t}_2$ equals

If 4x² + py² = 45 and x² - 4y² = 5 cut orthogonally, then the value of p is:

A line L is perpendicular to y = 2x + 10 such that it touches the parabola y² = 4(x – g). Then the distance between point of contact and origin is equal to

A circle x² + y² = 8 and a parabola y² = 2x are given. Find area bounded by these two curves in first quadrant which lie inside the circle and outside the parabola.

A parabola $y^2 = 12x$ has a chord PQ with mid-point (4, 1) then equation of PQ passes through