Question

The eccentricity of the ellipse $9x^2+4y^2-30y=0$ is $\frac{1}{p}\sqrt{q}$. Find the value $p$ and $q.$

• A. $p=2,q=2$
• B. $p=3,q=5$
• C. $p=2,q=5$
• D. $p=4,q=5$

Answer 1

The correct option is B $p=3,q=5$

Given ellipse may be written as,
$9x^2+4(y^2-\frac{15}{2}y+\frac{225}{16})=\frac{225}{4}$
or $\frac{x^2}{225/36}+\frac{{(y-15/4)}^2}{225/16}=1$
$\therefore b^2=\frac{225}{16},a^2=\frac{225}{36}$
$\therefore e^2=1-\frac{a^2}{b^2}=1-\frac{16}{36}=1-\frac{4}{9}=\frac{5}{9}$
$\therefore e=\frac{1}{3}\sqrt{5}.$