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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

AI Generated Solution

To solve the problem of finding the angle subtended by the common tangents of the two ellipses at the origin, we can follow these steps: ### Step 1: Write the equations of the ellipses The given ellipses are: 1. \( 4(x-4)^2 + 25y^2 = 100 \) 2. \( 4(x+1)^2 + y^2 = 1 \) We can rewrite these in standard form. ...
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