Question

Find the equation of parabola with vertex at the origin, axis along the X-axis and passing through the point(5,3).

Answer 1

Given that axis is along the x axis,

So, equation of parabola is of from

$y^2=4ac$ or $y^2=-4ax$

Since $(5,3)$ is in $1^{st}$ quadrant

So, the parabola will of the from

$y^2=4ax$

Point $(5,3)$ will satisfy the equation of

parabola

putting $x=5,y=3$ in equation

$(3{)}^2=4a(5)$

$y=20a$

$a=\frac{9}{20}$

Hence equation of parabola,

putting value of $a=\frac{9}{20}$ is

$y^2=4\times \left(\frac{9}{20}\right)\times x$

$y^2=\frac{9}{5}x$

$5y^2=9x$