A Ratio of Segments Range

★ 7/10Parametrization conic sections AM-GM analytic geometry

Problem

Consider the ellipse $C \colon \dfrac{x^2}{4} + \dfrac{y^2}{3} = 1$ . The line $l \colon my = x + 3m - 2$ passes through a fixed point $P$ and meets $C$ at two points $A, B$ with $|PA| < |PB|$ . Find the range of possible values of $\dfrac{|PA|}{|PB|}$ .

Answer

Solution

Difficulty	7/10
Topics	Parametrization, conic sections, AM-GM, analytic geometry

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