Question

If $P$ is any point on the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$and $S$ and $S$$\text{'}$ are the foci, then $\mathrm{PS}+{\mathrm{PS}}^{\text{'}}=$

• A. $4$
• B. $8$
• C. $10$
• D. $12$

Answer 1

The correct option is D

$12$

Explanation for the correct options:

Given, ellipse is $\frac{x^2}{36}+\frac{y^2}{16}=1$

Here $a^2=36,b^2=16$

As we know that, $a>b$ So the sum of the focal distance of any point $P$ on the ellipse is $\mathrm{PS}+{\mathrm{PS}}^{\text{'}}=2\mathrm{a}$

$\therefore \mathrm{PS}+\mathrm{PS}\text{'}=2\times 6$

$\therefore \mathrm{PS}+\mathrm{PS}\text{'}=12$

Hence option (d) is correct