New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Ellipse question

2025 · 2 Apr · Shift 2 · Q41

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Ellipse
2025 · 2 Apr · Shift 2 · Q41

Ellipse question

2025 · 2 Apr · Shift 2 · Q41

JEE MainMathematicsEllipseMCQ+4 / −1

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

A
$\frac{3}{\sqrt{19}}$
B
$\frac{\sqrt{3}}{16}$
C
$\frac{4}{\sqrt{17}}$
D
$\frac{\sqrt{5}}{7}$

More from Ellipse

A line passing through the point $P (5, 5)$ intersects the ellipse $\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1$ at $A$ and $B$ such that $(P A) \cdot (P B)$ is maximum. Then $5 (P A^{2} + P B^{2})$ is equal to :2025 · MCQ
Let $C$ be the circle of minimum area enclosing the ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ with eccentricity $\frac{1}{2}$ and foci $(\pm 2, 0)$ . Let $C$ be a variable triangle, whose vertex $P$ is on the circle $C$ and the…2025 · MCQ
The length of the latus-rectum of the ellipse, whose foci are $(2, - 3)$ and $(2, - 3)$ and eccentricity is $\frac{4}{5}$ , is2025 · MCQ
Let for two distinct values of p the lines $y = x + p$ touch the ellipse $E : \frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1$ 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…2025 · MCQ
The centre of a circle C is at the centre of the ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ . Let C pass through the foci $F_{1}$ and $F_{2}$ of E such that the circle $C$ and the…2025 · MCQ
Let the length of a latus rectum of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ be 10. If its eccentricity is the minimum value of the function $f (t) = t^{2} + t + \frac{11}{12}$ , $t \in R$ , then $a^{2} + b^{2}$ is equal to :2025 · MCQ
Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of P. If p + q = 126, then the…2025 · MCQ
Let the ellipse $3 x^{2} + p y^{2} = 4$ pass through the centre $C$ of the circle $x^{2} + y^{2} - 2 x - 4 y - 11 = 0$ of radius $r$ . Let $f_{1}, f_{2}$ be the focal distances of the point $C$ on the ellipse. Then $6 f_{1} f_{2} - r$ is equal to2025 · MCQ