iCON Education - Ellipse BITSAT Test

Question 1: Palette 1/3

BITSAT 2025 MCQ

Tangents are drawn to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at points where it is intersected by the line $l x+m y+n=0$. The point of intersection of tangents at these points is

A

$\left(\frac{a l}{n}, \frac{b m}{n}\right)$

B

$\left(\frac{a^2 l}{m}, \frac{b^2 m}{n}\right)$

C

$\left(\frac{b l}{n}, \frac{a m}{n}\right)$

D

$\left(\frac{-a^2 l}{n}, \frac{-b^2 m}{n}\right)$

Question 2: Palette 2/3

BITSAT 2025 MCQ

A rectangle is inscribed in an ellipse with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

What is the maximum area of the rectangle that can be inscribed in the ellipse?

A

$\frac{a b}{2}$

B

$a b$

C

$2 a b$

D

$\frac{a^2 b^2}{2}$.

Question 3: Palette 3/3

BITSAT 2020 MCQ

If the tangent at a point $\left( {4\cos \phi ,{{16} \over {\sqrt {11} }}\sin \phi } \right)$ to the ellipse $16{x^2} + 11{y^2} = 256$ is also a tangent to ${x^2} + {y^2} - 2x = 15$, then $\phi$ equsls

A

${\pi \over 3}$

B

${\pi \over 6}$

C

$-$${\pi \over 6}$

D

${\pi \over 4}$