List of top Mathematics Questions on Conic sections asked in JEE Main

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

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :

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

Let the tangent to the parabola $y^2 = 12x$ at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola $α^2 x^2 – 9y^2 = 9α^2$ at its point (α– 1, α + 2) is equal to__

If $y = m_1x + c_1 $and $y = m_2x + c_2$, $m_1≠m_2$ are two common tangents of circle $x_2 + y_2 = 2$ and parabola $y^2 = x$, then the value of $8|m_1m_2|$ is equal to :

Let the common tangents to the curves 4(x² + y²) = 9 and y² = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and I respectively denote the eccentricity and the length of the latus rectum of this ellipse, then
$\frac{1}{e^2}$ is equal to

A circle of radius 2 unit passes through the vertex and the focus of the parabola y² = 2x and touches the parabola $y=\left (x−\frac{1}{4}\right)^2+α,$ where $α > 0$. Then $(4α – 8)^2$ is equal to ___________.

Let $x=2t,\ y=\frac {t^2}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then $\lim\limits_{t \to 1} k$ is equal to

Let $Q$ be the mirror image of the point $P(1, 0, 1)$ with respect to the plane $S$: $x + y + z = 5$. If a line L passing through $(1, –1, –1)$, parallel to the line $PQ$ meets the plane $S$ at $R$, then $QR_2$ is equal to :

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of $7α + 3β$ is equal to ________ .

Let the tangent drawn to the parabola y² = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5. Then the normal to the hyperbola
$\frac{x^2}{α^2}−\frac{y^2}{β^2}=1$
at the point (α + 4, β + 4) does NOT pass through the point

An ellipse
$E:\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
passes through the vertices of the hyperbola
$H:\frac{x^2}{49} - \frac{y^2}{64} = -1$
Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If the length of the latus rectum of the ellipse E, then the value of 113l is equal to _____.