First slide

Ellipse

Question

$Equation of the ellipse having centre at origin and touching the hyperbola \frac{x^{2}}{25} - \frac{y^{2}}{16} = 1 at its$ $vertices and having eccentricity 3/5 is$

Moderate

A

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

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

$\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1$
D

$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$

Solution

$\begin{array}{l} a = 5 \\ b^{2} = a^{2} (1 - e^{2}) = 25 (1 - \frac{9}{25}) = 16 . \\ \Rightarrow b = 4 \\ ∴ \frac{x^{2}}{25} + \frac{y^{2}}{16} = 1 \end{array}$

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