Question

The sum of the focal distances of any point on the ellipse 9x² + 16y² = 144 is
(a) 32
(b) 18
(c) 16
(d) 8

Answer 1

$$\begin{gathered} \left(\mathrm{d}\right)8 \\ {\mathrm{9x}}^2{+\; 16y}^2=\; 144 \\ \Rightarrow \frac{x^2}{16}+\frac{y^2}{9}=1 \\ \text{Here,}\mathit{\text{a}}\text{=4 and}\mathit{\text{b}}\text{=3} \\ \text{The sum of the focal distances of any point on an ellipse is constant and equal to the length of the major axis of the ellipse.} \\ \mathrm{i}.\mathrm{e}.\mathrm{sum\; of\; the\; focal\; distances\; of\; any\; point\; on\; an\; ellips}e=2a \\ =2\times 4 \\ =8 \end{gathered}$$