Question

The distances from the foci of $P (x_1, y_1)$on the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ are

• A. $4 \pm \frac{5}{4}y_1$
• B. $5 \pm \frac{4}{5}y_1$
• C. $4 \pm \frac{4}{5}y_1$
• D. None of these.

Answer 1

Answer: (B)

Focal distance of $\left(x_{1}, y_{1}\right)$ are $b\pm ex_{1} $
$ \left[a^{2}=9\Rightarrow a=3, b^{2}=25\Rightarrow b=5\right] $
Since $a^{2}= b^{2}\left(1-e^{2}\right)$
$ 9=25\left(1-e^{2}\right) $
$\Rightarrow 1-e^{2} = \frac{9}{25} $
$ \Rightarrow e^{2} = \frac{16}{25}$
$ \Rightarrow e=\frac{4}{5}$
$\therefore $ focal distance $= 5\pm\frac{4}{5}x_{1}$