Question

The sum of the distance of any point on the ellipse $4x^2+9y^2=36$ from $(\sqrt{5},0)$ and $(-\sqrt{5},0)$ is:

• A. $6$
• B. $4$
• C. $18$
• D. $8$

Answer 1

The correct option is B $4$

An ellipse with its center at the origin can also have its major axis on the $y-$axis.In this case the sum of the distances from any point $P$ on the ellipse to the foci is set equal to the constant $2b$

From the equation $4x^2+9y^2=36$

$\Rightarrow \frac{x^2}{9}+\frac{y^2}{4}=1$ shown equation of ellipse where $a=3$ and $b=2$

We have $a>b$

$\therefore$ Sum of the distances from any point $P$ is $2b=2\times 2=4$ units