Question

Find the equation of a parabola with vertex at the origin, the axis along X-axis and passing through $(2,3).$

• A. $2x^2=9y$
• B. $2y^2=9x$
• C. $6y^2-27x=0$
• D. $6x^2-27y=0$

Answer 1

Answer: (B), (C)

The correct options are
B $2y^2=9x$
C $6y^2-27x=0$

Equation of the parabola, $y^2=4ax$.
Since, it passes through $(2,3)$, $a=\frac{9}{8}$
$\therefore$ Equation of the parabola,
$y^2=44\left(\frac{9}{8}\right)x$
$6y^2-27x=0$

$\Rightarrow 2y^2=9x$