A Tangent Collinearity

★ 8/10Parametrization Circles conic sections analytic geometry

Problem

Consider the ellipse $C \colon \dfrac{x^2}{9} + \dfrac{y^2}{8} = 1$ and the circle $M \colon x^2 + 2x + y^2 + m = 0$ . A line through the left vertex $A$ of the ellipse is tangent to the circle $M$ at $B$ and meets the ellipse again at $P$ . The line joining $P$ to the right focus $F$ meets the ellipse again at $Q$ . If $B, M, Q$ are collinear, find the real number $m$ .

Answer

Solution

Difficulty	8/10
Topics	Parametrization, Circles, conic sections, analytic geometry

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