Tangent Are Drawn From Any Point On The Hyperbola  to The Circle x2 + y2 = 9. If The Locus Of The Mid-point Of The Chord Of Contact Is   

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Tangent are drawn from any point on the hyperbola  to the circle x2 + y2 = 9. If the locus of the mid-point of the chord of contact is



Correct option is


Equation of the chord of contact of a point  on the hyperbola is with respect to the circle is

                  … (1)

Let M(h, k) be the mid-point of (1), then equation of (1) in terms of the mid-point is

      hx + ky = h2 + k2

Since (1) and (2) represent the same line.


 Locus of (h, k) is


or  4(x2 + y2)2 = 36x2 – 81y2

which is same as a(x2 + y2)2 = bx2 – cy2

 = 4, b = 36, c = 81

     a2 + b2 + c2 = 16 + 1296 + 6561 = 7873.



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