Question

P is any point on the ellipse $9x^2+36y^2=324$ whose foci are S and S'. Then $SP+S^{\prime }P$ equals?

• A. $3$
• B. $12$
• C. $36$
• D. $324$

Answer 1

Answer: (B)

$12$

Formula,

$SP+S^{\prime }P=2a$

given,

$9x^2+36y^2=324$

$\Rightarrow \frac{x^2}{\frac{324}{9}}+\frac{y^2}{\frac{324}{36}}=1$

$\therefore a^2=\frac{324}{9}$

$\Rightarrow a=\frac{18}{3}=6$

$\Rightarrow SP+S^{\prime }P=2a=2\times 6=12$