The acute angle between the pair of tangents | vedclass

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Question

Equation of tangent to the ellipse $2 x ^{2}+3 y ^{2}=5$ is

$y = mx \pm \sqrt{\frac{5}{2} m ^{2}+\frac{5}{3}}$

It pass through $(1,3)$

$3=m \

Vedclass · Accepted Answer

$	an ^{-1}\left(\frac{24}{7 \sqrt{5}}ight)$

Vedclass · Answer

Equation of tangent to the ellipse $2 x ^{2}+3 y ^{2}=5$ is

$y = mx \pm \sqrt{\frac{5}{2} m ^{2}+\frac{5}{3}}$

It pass through $(1,3)$

$3=m \pm \sqrt{\frac{5}{2} m^{2}+\frac{5}{3}}$

$3\,m^{2}+12\,m-\frac{44}{3}=0$

Let $	heta$ be the angle between the tangents

$	an 	heta=\left|\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}ight|$

$	an 	heta=\left|\frac{3 \sqrt{320}}{-35}ight|$

$	heta=	an ^{-1}\left(\frac{24}{7 \sqrt{5}}ight)$

The acute angle between the pair of tangents drawn to the ellipse $2 x^{2}+3 y^{2}=5$ from the point $(1,3)$ is.

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