Tangents are drawn from any point on the hyperbola `(x^2)/9-(y^2)/4=1` to the circle `x^2+y^2=9` . Find the locus of the midpoint of the chord of contact.

Explanation

Let the midpoint of chord of contact is`(h,k)`

Parametric point on given hyperbola is`P(3sectheta, 2tantheta)`

Equation of tangent to given circle from the point P is,

`T=0`

`3xsectheta +2ytantheta=9 => (1)`
Equation of tangent with the mid point(h,k) to the circle `x^2+y^2=9` is

`T=S1`

`hx+ky-9=h^2+k^2-9`

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