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  4. If the chord through the point whose eccentric angles are θ φ on the ellipse, ( x 2 / a 2)+( y 2 / b 2)=1 passes through the focus, then the value of (1+ e ) tan (θ / 2) tan (φ / 2) is

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Q. If the chord through the point whose eccentric angles are $\theta \& \phi$ on the ellipse, $\left( x ^2 / a ^2\right)+\left( y ^2 / b ^2\right)=1$ passes through the focus, then the value of $(1+ e ) \tan (\theta / 2) \tan (\phi / 2)$ is

Conic Sections

Solution:

Chord: $\frac{ x }{ a } \cos \left(\frac{\theta+\phi}{2}\right)+\frac{ y }{ b } \sin \left(\frac{\theta+\phi}{2}\right)=\cos \left(\frac{\theta-\phi}{2}\right)$