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Options

A. `(a^(2)+b^(2))/(a)`
B. `-(a^(2)+b^(2))/(a)`
C. `(a^(2)+b^(2))/(b^(2))`
D. `-(a^(2)+b^(2))/(b)`

Explanation

The coordinates `(h,k)` of the point of intersection of the normals at `P` and `Q` are given by
`h=-((a^(2)+b^(2))/(a))(cos((theta-phi)/(2))costhetacosphi)/(cos((theta+phi)/(2)))`
and, `k=-((a^(2)+b^(2))/(a))tan((theta+phi)/(2))tanthetatanphi`.
We have, `theta+phi=(pi)/(2)`
`k=-((a^(2)+b^(2))/(b))tan.(pi)/(4)tanthetacotthetaimpliesk=-((a^(2)+b^(2))/(b))`