Question

The sum of the focal distances from any point on the ellipse $9x^2+16y^2=144$is

• A. $3$
• B. $6$
• C. $8$
• D. $4$

Answer 1

The correct option is C

$8$

Explanation for the correct option

Equation of given ellipse is $9x^2+16y^2=144$

$\Rightarrow \frac{x^2}{16}+\frac{y^2}{9}=1$

In comparison with the general form of the ellipse

$$\begin{gathered} a^2=16,b^2=9 \\ \Rightarrow a=4,b=3 \end{gathered}$$

Now, the length of the major axis is $=2a=2\times 4=8$

$\because$ The sum of focal length at any point on the ellipse equal to the major axis

So, the sum of focal length at any point on the ellipse $=8$

Hence, the correct option is C.