If centre, one of foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5 then its equation i

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10-2. Parabola, Ellipse, Hyperbola

easy

If the centre, one of the foci and semi-major axis of an ellipse be $(0, 0), (0, 3)$ and $5$ then its equation is

A

$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1$

B

$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$

C

$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{25}} = 1$

D

None of these

Solution

(a) Centre $(0,0)$, focus $(0,3)$, $b = 5$

Focus $(0,3)$ ==> $be = 3$

==> $e = 3/5$ ==> $a = b\sqrt {1 – {e^2}} = 4$

Hence the required equation is $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1$.

Standard 11

Mathematics

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