Consider a curve \( a x^{2}+2 h x y+b y^{2}=1 \) and a point \( P \...

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Consider a curve \( a x^{2}+2 h x y+b y^{2}=1 \) and a point \( P \)
\( \mathrm{P} \) not on the curve. A line drawn from the point \( P \)

W intersects the curve at points \( Q \) and \( R \). If the product \( P Q \cdot P R \) is independent of the slope of the line, then show that the curve is a circle.
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