Equation of ellipse whose one of vertices is (0,7) and corresponding directrix is y = 12 , is

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10-2. Parabola, Ellipse, Hyperbola

easy

The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y = 12$, is

A

$95{x^2} + 144{y^2} = 4655$

B

$144{x^2} + 95{y^2} = 4655$

C

$95{x^2} + 144{y^2} = 13680$

D

None of these

Solution

(b) Vertex $(0,7)$, directrix $y = 12$, $b = 7$

Also $\frac{b}{e} = 12$

$e = \frac{7}{{12}},\;a = 7\sqrt {\frac{{95}}{{144}}} $

Hence equation of ellipse is $144{x^2} + 95{y^2} = 4655$.

Standard 11

Mathematics

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