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 $b\pm e{x}_1$
$\left[a^2=9\Rightarrow a=3,b^2=25\Rightarrow b=5\right]$
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 $=5\pm \frac{4}{5}{x}_1$