Equation of ellipse whose one focus is at (4, 0) and whose eccentricity is 4/5 , is

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10-2. Parabola, Ellipse, Hyperbola

easy

The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$, is

A

$\frac{{{x^2}}}{{{3^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$

B

$\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{3^2}}} = 1$

C

$\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{4^2}}} = 1$

D

$\frac{{{x^2}}}{{{4^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$

Solution

(b) Here $ae = 4 $and$ e = \frac{4}{5} \Rightarrow a = 5$

Now ${b^2} = {a^2}(1 – {e^2}) \Rightarrow {b^2} = 25\left( {1 – \frac{{16}}{{25}}} \right) = 9$

Hence equation of the ellipse is $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$.

Standard 11

Mathematics

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