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  • Let a circle of radius 4 be concentric to the ellipse . Then the common tan

Let a circle of radius 4 be concentric to the ellipse 15 x^2+19 y^2=285. Then the common tangents are inclined to the minor axis of the ellipse at the angle.

Option: 1

\frac{\pi}{6}


Option: 2

\frac{\pi}{12}


Option: 3

\frac{\pi}{3}


Option: 4

\frac{\pi}{4}


Answers (1)

best_answer

\frac{x^2}{19}+\frac{y^2}{15}=1

Let tang be

$$ \begin{aligned} & y=m x \pm \sqrt{19 m^2+15} \\ & m x-y \pm \sqrt{19 m^2+15}=0 \end{aligned}
Parallel from (0,0)=4
$$ \begin{aligned} & \left|\frac{ \pm \sqrt{19 m^2+15}}{\sqrt{m^2+1}}\right|=4 \\ & 19 m^2+15=16 m^2+16 \\ & 3 m^2=1 \\ & m= \pm \frac{1}{\sqrt{3}} \\ & \theta=\frac{\pi}{6} \text { with x-axis } \end{aligned}
Required angle \frac{\pi}{3}.

Posted by

Devendra Khairwa

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