Two Perpendicular Focal Vectors

★ 7/10Law of Cosines conic sections vectors

Problem

The hyperbola $C:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ ( $a>0$ , $b>0$ ) has left and right foci $F_1$ , $F_2$ . A point $A$ lies on $C$ and a point $B$ lies on the $y$ -axis, with

\overrightarrow{F_1A}\perp\overrightarrow{F_1B},\qquad \overrightarrow{F_2A}=-\frac 23\overrightarrow{F_2B}.

Find the eccentricity of $C$ .

Answer

Solution

Difficulty	7/10
Topics	Law of Cosines, conic sections, vectors

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