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The locus of the point of intersection o...

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola `xy=c^2` is (A) `(x^2-y^2 )^2 + 4c^2xy = 0` (B)` (x^2+y^2)^2+ 4c2^xy=0` (C)` x^2-y^2 )^2 + 4cxy = 0` (D) `(x^2 +y^2)^2+4cxy =0`

Text Solution

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Equation of tangent to hyperbola `xy=c^2` is:
`x(x1)+y(y1)=2c^2 => (1)` Equation of normal chord at point(h,K) will be:
`hx-ky=h^2-k^2 => (2)` On equating (1) and (2), we get
`h/(x1)=-k/(y1)=(h^2-k^2)/(2c^2)`
On solving,The locus is:
`(x^2-y^2)^2+4c^2xy=0`
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