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The locus of the image of the focus of t...

The locus of the image of the focus of the ellipse `(x^2)/(25)+(y^2)/9-1,(a > b),` with respect to any of the tangents to the ellipse is `(x+4)^2+y^2=100` (b) `(x+2)^2+y^2=50` `(x-4)^2+y^2=100` (d) `(x+2)^2+y^2=50`

A

`(x+4)^(2)+y^(2)=100`

B

`(x+2)^(2)+y^(2)=50`

C

`(x-4)^(2)+y^(2)=100`

D

`(x-2)^(2)+y^(2)=50`

Text Solution

Verified by Experts

Let S''(h,k)be the image.
SS'' cuts a tangents at a point which lies on the auxiliary circle of the ellipse. Therefore,
`((h+-4)/(2))+(k^(2))/(4)=25`
Hence the locus is `(x+-4)+y^(2)=100`
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