Eccentricity of an ellipse is 2/3 , latus rectum is 5 and centre is (0, 0) . equation of ellipse is

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10-2. Parabola, Ellipse, Hyperbola

easy

The eccentricity of an ellipse is $2/3$, latus rectum is $5$ and centre is $(0, 0)$. The equation of the ellipse is

A

$\frac{{{x^2}}}{{81}} + \frac{{{y^2}}}{{45}} = 1$

B

$\frac{{4{x^2}}}{{81}} + \frac{{4{y^2}}}{{45}} = 1$

C

$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$

D

$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

Solution

(b) ${\left( {\frac{2}{3}} \right)^2} = 1 – \frac{{{b^2}}}{{{a^2}}}$ and $\frac{{2{b^2}}}{a} = 5$

$a = \frac{{81}}{4}$, $b = \frac{{45}}{4}$

Hence the equation is $\frac{{4{x^2}}}{{81}} + \frac{{4{y^2}}}{{45}} = 1$.

Standard 11

Mathematics

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