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Any ordinate M P of the ellipse (x^2)/(2...

Any ordinate `M P` of the ellipse `(x^2)/(25)+(y^2)/9=1` meets the auxiliary circle at `Qdot` Then locus of the point of intersection of normals at `Pa n dQ` to the respective curves is (a)`x^2+y^2=8` (b) `x^2+y^2=34` (c)`x^2+y^2=64` (d) `x^2+y^2=15`

A

`x^(2)+y^(2)=8`

B

`x^(2)+y^(2)= 34`

C

`x^(2)+y^(2)= 64`

D

`x^(2)+y^(2)= 15`

Text Solution

Verified by Experts

The equation of normal of normal to the ellipse at P is
`5x sec, theta-3y"cosec"theta=16`
The equation of normal to the circel `x^(2)+y^(2)=25` at point Q is `y=x tan theta " "(2)`

The eliminating `theta` from (1) and (2) we, get `x^(2)+y^(2)=64`
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