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Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola `16y^2 -9 x^2 = 1` is

A

`x^(2)+y^(2)=9`

B

`x^(2)+y^(2)=1//9`

C

`x^(2)+y^(2)=7//144`

D

`x^(2)+y^(2)=1//16`

Text Solution

Verified by Experts

The correct Answer is:
D
`(y^(2))/(1//16)-(x^(2))/(1//9)=1`
Locus will be the auxiliary circle
`x^(2)+y^(2)=(1)/(16)`
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