Question

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0,0) passing through (2,3) and axis is along x - axis.

Answer 1

The vertex of the parabola is at (0,0) and the axis is along x axis.
So the parabola is of the form $y^2=4ax$.
Since the parabola passes through point (2,3)
$\therefore (3{)}^2=4a\times 2\Rightarrow 9=8a\Rightarrow a=\frac{9}{8}$
The required equation of parabola is,
$y^2=\frac{4\times 9}{8}x\Rightarrow y^2=\frac{9}{2}x\Rightarrow 2y^2=9x$