Locus of point of intersection of two perpendicular tangent of ellipse frac{{{x^2}}

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10-2. Parabola, Ellipse, Hyperbola

normal

The locus of point of intersection of two perpendicular tangent of the ellipse $\frac{{{x^2}}}{{{9}}} + \frac{{{y^2}}}{{{4}}} = 1$ is :-

A

$x^2 + y^2 = 4$

B

$x^2 + y^2 = 9$

C

$x^2 + y^2 = 13$

D

$x^2 + y^2 = 5$

Solution

Locus of point of intersection of two perpendicular tangent's of the ellipse is director circle and equation is

$\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}$

So, $x^{2}+y^{2}=9+4 \Rightarrow x^{2}+y^{2}=13$

Standard 11

Mathematics

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