Consider a curve and a point not on the curve

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider a curve

ax^2 + 2hxy + by^2 = 1

and a point

P

not on the curve. A line drawn from the point

P

intersects the curve at points

Q

and

R

. If the product

PQ \cdot PR

is independent of the slope of the line, then show that the curve is a circle.