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.