Question

Find the equation of the ellipse in the case:

Vertices (0, ± 13), foci (0, ± 5)

 

Answer 1

\[ \text{ Vertices } \left( 0, \pm 13 \right)\text{ and focus } \left( 0, \pm 5 \right)\]
\[\text{ The coordinates of its vertices and foci are } \left( 0, \pm b \right)\text{ and } \left( 0, \pm be \right), \text{ respectively.} \]
\[i . e . b = 13\text{  and be } = 5\]
\[ \therefore e = \frac{5}{13}\]
\[\text{ Now } , a^2 = b^2 \left( 1 - e^2 \right)\]
\[ \Rightarrow a^2 = 169\left( 1 - \frac{25}{169} \right)\]
\[ \Rightarrow a^2 = 144\]
\[ \therefore \frac{x^2}{144} + \frac{y^2}{169} = 1\]
\[\text{ Thisis the required equation of the ellipse } .\]