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The angle subtended by common tangents o...

The angle subtended by common tangents of two ellipses `4(x-4)^2+25 y^2=100a n d4(x+1)^2+y^2` at the origin is `pi/3` (b) `pi/4` (c) `pi/6` (d) `pi/2`

A

`pi//3`

B

`pi//4`

C

`pi//6`

D

`pi//2`

Text Solution

Verified by Experts

`((x-4)^(2))/(25)+(y^(2))/(4)=1 and (x+1)^(2)+(y^(2))/(4)=1`.
Clearly , `m_(OP)*m_(OQ)=-1`
Therefore, OP and QP are pependicular to each other
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