A Focal Chord Invariant

★ 7/10Parametrization conic sections analytic geometry

Problem

A line $l$ through the focus $F$ of the parabola $C \colon y^2 = 2px$ meets $C$ at $A$ and $B$ , and meets the $y$ -axis at $P$ . If

\overrightarrow{PA} = \lambda\overrightarrow{AF}, \qquad \overrightarrow{PB} = \mu\overrightarrow{BF},

find $\lambda + \mu$ .

Answer

Solution

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

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