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.

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