Conic problem!

Geometry Level 4

\(P\) And \(Q\) are two variable points on the rectangular hyperbola

\(xy = c^2\) such that the tangent at \(Q\) passes through the foot of

ordinate of \(P \). if the locus of point of intersection of tangents at P And

\(Q \) is the hyperbola \(xy= kc^2\). Find the value of \(9k\).

Clarification- Foot of ordinate means foot of perpendicular from the point to the \(x\)-axis.

For the problem writing party


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