JEE MAIN Ellipse Previous Year Questions (PYQs) – Page 1 of 5

The length of the chord of the ellipse $\dfrac{x^{2}}{4}+\dfrac{y^{2}}{2}=1$ whose midpoint is $\left(1,\dfrac{1}{2}\right)$ is:

The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2}+3y^{2}=6$ on any tangent to it is :

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity ${1 \over 3}$ and the distance of the nearer focus from this directrix is ${8 \over {\sqrt {53} }}$, then the equation of the other directrix can be :

Let for two distinct values of $p$ the lines $y=x+p$ touch the ellipse $E:\ \dfrac{x^{2}}{4^{2}}+\dfrac{y^{2}}{3^{2}}=1$ at the points $A$ and $B$. Let the line $y=x$ intersect $E$ at the points $C$ and $D$. Then the area of the quadrilateral $ABCD$ is

The centre of a circle $C$ is at the centre of the ellipse $E:\ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1,\ a>b$. Let $C$ pass through the foci $F_{1}$ and $F_{2}$ of $E$ such that the circle $C$ and the ellipse $E$ intersect at four points. Let $P$ be one of these four points. If the area of the triangle $PF_{1}F_{2}$ is $30$ and the length of the major axis of $E$ is $17$, then the distance between the foci of $E$ is

An ellipse, with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$, passes through which of the following points?

Let the product of the focal distances of the point $\left( \sqrt{3}, \dfrac{1}{2} \right)$ on the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, $(a > b)$, be $\dfrac{7}{4}$. Then the absolute difference of the eccentricities of two such ellipses is

The length of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$, whose midpoint is $\left(1,\dfrac{9}{5}\right)$, is equal to:

In a group of 100 persons, 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons who speak only English is $\alpha$ and the number of persons who speak only Hindi is $\beta$, then the eccentricity of the ellipse \[ 25\big(\beta^2 x^2 + \alpha^2 y^2\big)=\alpha^2\beta^2 \] is:

Let the length of the latus rectum of an ellipse with its major axis along the $x$-axis and centre at the origin be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?