Question

Find length of latus rectum and vertices respectively of the ellipse $9x^{2} + 2 5 y^{2} = 225$.

• A. $\frac{18}{5}, \left(\pm 5, 0\right)$
• B. $\frac{5}{18}, \left(\pm 5, 0\right)$
• C. $\frac{5}{6}, \left(\pm 5, 2\right)$
• D. $\frac{5}{18}, \left(0, \pm5\right)$

Answer 1

Answer: (A)

The given equation can be rewritten as
$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$
This shows that $a = 5$ and $b = 3$. Hence length of latus rectum $=\frac{2b^{2}}{a}=\frac{18}{5}$ and vertices are $\left(5,0\right)$ and $\left(-5,0\right)$.