Question

The sum of the focal distances of any point on the ellipse 9x² + 16y² = 144 is

Options

• 32

• 18

• 16

• 8

Answer 1

 8
\[ {9x}^2 {+ 16y}^2 = 144 \]
\[ \Rightarrow \frac{x^2}{16} + \frac{y^2}{9} = 1\]
\[\text{ Here, }a=4\text{ and }b=3\]
The sum of the focal distances of any point on an ellipse is constant and equal to the length of the major axis of the ellipse.
i . e . sum of the focal distances of any point on an ellipse = 2a
\[ = 2 \times 4\]
\[ = 8\]