A Section Ratio Range

★ 7/10conic sections analytic geometry Vieta's Formulas Discriminant

Problem

A line $l$ through $P(0, 2)$ meets the ellipse $\dfrac{x^2}{5} + y^2 = 1$ at points $M$ and $N$ , and $\overrightarrow{PM} = \lambda\overrightarrow{PN}$ . Find the range of possible values of $\lambda$ .

Answer

Solution

Difficulty	7/10
Topics	conic sections, analytic geometry, Vieta's Formulas, Discriminant

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