Four Points in Order

★ 7/10Parametrization Substitution conic sections analytic geometry

Problem

A line $\ell$ meets the ellipse $\dfrac{x^2}{4} + \dfrac{y^2}{2} = 1$ at $A$ and $B$ , the negative $x$ -axis at $C$ , and the positive $y$ -axis at $D$ , with $A, C, D, B$ in order along $\ell$ and

|AC| = |CD| = 2|DB|.

Find the slope of $\ell$ .

Answer

Solution

Difficulty	7/10
Topics	Parametrization, Substitution, conic sections, analytic geometry

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