First slide

Ellipse

Question

$Let P_{i} and P_{i}^{'} be the feet of the perpendicular drawn from the foci S and S^{'} on a tangent T_{i}$ $to an ellipse whose length of semi major axis is 20. If \sum_{i = 1}^{10} (S P_{i}) (S' P_{i}^{1}) = 2560, then the value$ of the eccentricity is

Difficult

A

$\frac{1}{2}$
B

$\frac{2}{5}$
C

$\frac{3}{5}$
D

$\frac{4}{5}$

Solution

Product of length of perpendiculars from foci on a tangent to the ellipse=b2
$∴ (S P_{1}) (S^{1} P_{1}^{1}) = (S P_{2}) (S^{1} P_{2}^{1}) = ......... = (S P_{10}) (S^{1} P_{10}^{1}) = b^{2}$
$\sum_{i = 1}^{10} (S P_{i}) (S^{1} P_{i}^{1}) = 2560$
$10 b^{2} = 2560 \Rightarrow b^{2} = 256, \Rightarrow b = 16$
b2= a2(1- e2)
$16^{2} = 20^{2} (1 - e^{2}) \Rightarrow e = 3 / 5$

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