Question

The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y=12$ is

• A. $95 x^2+144 y^2=4655$
• B. $144 x^2+95 y^2=4655$
• C. $95 x^2+144 y^2=13680$
• D. None of the above

Answer 1

Answer: (B)

Given that, vertex $(0,7)$, directrix $y=12$ of an ellipse.
$\therefore b-7$
$\text { Also, } \frac{b}{e}=12$
$\Rightarrow e=\frac{7}{12}, a=7 \sqrt{\frac{95}{144}}$
Hence, equation of ellipse is $144 x^2+95 y^2=4655$