Question

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

Answer 1

Let the equation of parabola be $y^2=4ax$ ...(i)

$[\because axisaolngx-axis]$

If passes through (2,3)

$\therefore (3{)}^2=4\times a\times 2\Rightarrow 9=8a\Rightarrow a=\frac{9}{8}$

Putting the value of a in equation (i),we get

$y^2=4\times \frac{9}{8}\times x\Rightarrow y^2=\frac{9}{2}\times x\Rightarrow 2y^2=9x$

Hence,the required equation of parabola is $2y^2=9x.$