If lines 3x + 2y = 10 and -3x + 2y = 10 are t | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

tangent $\frac{\mathrm{x}}{\mathrm{b}}+\frac{\mathrm{ye}}{\mathrm{b}}=1$

Vedclass · Accepted Answer

$\frac{{100}}{{27}}$

Vedclass · Answer

Let ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

tangent $\frac{\mathrm{x}}{\mathrm{b}}+\frac{\mathrm{ye}}{\mathrm{b}}=1$

$	herefore \frac{b}{e}=5$

and $b=\frac{10}{3} \Rightarrow e=\frac{2}{3}$

$\Rightarrow \mathrm{a}^{2}=\frac{500}{81} \quad 	herefore \mathrm{L} \cdot \mathrm{R}=\frac{2 \mathrm{a}^{2}}{\mathrm{b}}=\frac{100}{27}$

If lines $3x + 2y = 10$ and $-3x + 2y = 10$ are tangents at the extremities of latus rectum of an ellipse whose centre is origin, then the length of latus rectum of ellipse is

Similar Questions

What is the equation of the ellipse with foci $( \pm 2,\;0)$ and eccentricity $ = \frac{1}{2}$

If the midpoint of a chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ is $(\sqrt{2}, 4 / 3)$, and the length of the chord is $\frac{2 \sqrt{\alpha}}{3}$, then $\alpha$ is :

The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is

Eccentricity of the ellipse $4{x^2} + {y^2} - 8x + 2y + 1 = 0$ is

An ellipse has $OB$ as semi minor axis, $F$ and $F'$ its foci and the angle $FBF'$ is a right angle. Then the eccentricity of the ellipse is