A Slope from a Product Ratio

★ 8/10Parametrization conic sections analytic geometry Vieta's Formulas

Problem

A line through $P(1,1)$ meets the left and right branches of the hyperbola $\dfrac{x^2}4-\dfrac{y^2}5=1$ at points $A$ and $B$ respectively, with

\frac{|PA|\cdot|PB|}{|AB|}=\frac{19\sqrt{10}}{20}.

Find the slope of the line $AB$ .

Answer

Solution

Difficulty	8/10
Topics	Parametrization, conic sections, analytic geometry, Vieta's Formulas

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