Question

Find the equation of the ellipse in the following case:  

Foci (± 3, 0), a = 4

Answer 1

\[\text{ Foci }=\left( \pm 3, 0 \right)\text{ and }a=4\]
\[\text{ i . e } . ae = 3\]
\[ \Rightarrow e = \frac{3}{4}\]
\[\text{ Now }, e = \sqrt{1 - \frac{b^2}{a^2}}\]
\[ \Rightarrow \frac{3}{4} = \sqrt{1 - \frac{b^2}{16}}\]
\[\text{ On squaring both sides, we get }:\]
\[\frac{9}{16} = \frac{16 - b^2}{16}\]
\[ \Rightarrow b^2 = 7\]
\[ \therefore \frac{x^2}{16} + \frac{y^2}{7} = 1\]
\[\text{ This is the required equation of the ellipse }.\]