A chord PQ of the hyperbola `xy=c^2` is tangent to the hyperbola `x^2 / a^2 - y^2 / b^2 = 1` Find the locus of the middle point of PQ.

Explanation

Given, hyperbola `xy = c^2`
Let its chord `PQ` has the mid point `(h,k)`
`Eqn.` of chord with a given point
`T = S_1`
From eqn. of hyperbola, tangent:
`T= 2*xy/2 = c^2`
`rArr T = (xy + xy)/2 - c^2`
At point `(h,k)`
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