Question

The equation of the parabola whose vertex is at the centre of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and the focus coincide with the focus of the ellipse on the positive side of the major axis of the ellipse is

• A. $y^2=3x$
• B. $y^2=4x$
• C. $y^2=5x$
• D. $y^2=12x$

Answer 1

The correct option is D $y^2=12x$

Equation of ellipse is $\frac{x^2}{25}+\frac{y^2}{16}=1$

$a=5,b=4e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

focus is $(ae,0)=(5\times \frac{3}{5},0)=(3,0)$

focus of parabola is at $(3,0)$

$\therefore a=3$

and vertex is at $(0,0)$

$\therefore$ equation of parabola is $y^2=4ax$

$y^2=4\times 3x{y}^2=12x$