Normal are drawn to the hyperbola a2x2−b2y2=1 at point θ1andthη2 meeting the conjugate axis at G1andG2, respectively. If θ1+θ2=2π, prove that CG1C˙G2=e2−1a2e4 , where C is the center of the hyperbola and e is the eccentricity.

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Question

Normal are drawn to the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ at point $θ_{1} a n d t h η_{2}$ meeting the conjugate axis at $G_{1} a n d G_{2},$ respectively. If $θ_{1} + θ_{2} = \frac{π}{2},$ prove that $C G_{1} \dot{C} G_{2} = \frac{a ^{2} e ^{4}}{e ^{2} - 1}$ , where $C$ is the center of the hyperbola and $e$ is the eccentricity.

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Harper Discussed

Normal are drawn to the hyperbola

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

at point

θ_{1} a n d t h η_{2}

meeting the conjugate axis at

G_{1} a n d G_{2},

respectively. If

θ_{1} + θ_{2} = \frac{π}{2},

prove that

C G_{1} \dot{C} G_{2} = \frac{a ^{2} e ^{4}}{e ^{2} - 1}

, where

C

is the center of the hyperbola and

e

is the eccentricity.

14 mins ago

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