A Focal Ratio on an Ellipse

★ 7/10trigonometry Trigonometric Identities conic sections Symmetry

Problem

$F_1, F_2$ are the foci of $C: \dfrac{x^2}{4} + \dfrac{y^2}{3} = 1$ . Points $A(x_1, y_1)$ , $B(x_2, y_2)$ on $C$ satisfy $x_1 + x_2 = \dfrac12$ and

\overrightarrow{AF_2} = \lambda\,\overrightarrow{F_2B}.

Find $\lambda$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Trigonometric Identities, conic sections, Symmetry

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