First slide

Ellipse

Question

$Length of the perpendicular from the centre of the ellipse 27 x^{2} + 9 y^{2} = 243 on a tangent drawn to it which makes$
$equal intercepts on the coordinates axes is$

Moderate

A

$\frac{3}{2}$
B

$\frac{3}{\sqrt{2}}$
C

$3 \sqrt{2}$
D

6

Solution

$Ellipse \frac{x^{2}}{9} + \frac{y^{2}}{27} = 1$
$Tangent to ellipse having slope m is y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$
$Since tangent makes equal intercepts on the coordinate axes, m=-1$
$∴ Equation of tangents are y = - x \pm 6 or x + y \pm 6 = 0$
$Length of perpendicular from (0, 0) = |\frac{6}{\sqrt{2}}| = 3 \sqrt{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App