The equation of the ellipse with e =3/4  , foci on y-axis, centre of the origin and passing through the point (6, 4) is

Q: The equation of the ellipse with e =3/4  , foci on y-axis, centre of the origin and passing through the point (6, 4) is

(A) x² + 2y² = 16

(B) 16x² + 7y² = 688

(C) 16x² + 7y² = 344

(D) none of these

Sol: $\large b^2 = a^2 (1-\frac{9}{16}) = \frac{7}{16}a^2 $

Then equation is $\large \frac{16 x^2}{7 a^2} + \frac{y^2}{a^2} = 1 $ , it passes through (6, 4)

$\large \frac{16 \times 6^2}{7 a^2} + \frac{16}{b^2} = 1 $

$\large a^2 = \frac{688}{7}$

16x² + 7y² = 688 is ellipse.