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

Question

The equation of the ellipse whose one of the vertices is (0,7) and the corresponding directrix is y=12 is (A) 95 x2+144 y2=4655 (B) 144 x2+95 y2=4655 (C) 95 x2+144 y2=13680 (D) None of the above

Tardigrade Admin · Accepted Answer

Given that, vertex (0,7), directrix y=12 of an ellipse. ∴ b-7 text Also, (b/e)=12 ⇒ e=(7/12), a=7 √(95/144) Hence, equation of ellipse is 144 x2+95 y2=4655

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

$95 x^{2} + 144 y^{2} = 4655$

$144 x^{2} + 95 y^{2} = 4655$

$95 x^{2} + 144 y^{2} = 13680$

None of the above

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

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

95x2+144y2=4655

144x2+95y2=4655

95x2+144y2=13680