Question

A parabola has its vertex at the origin; its axis lies along the x-axis and it passes through the point $P(2,3)$. The equation of the parabola is

• A. $4y^2=9x$
• B. $y^2=\frac{4}{9}x$
• C. $y^2=\frac{9}{2}x$
• D. $y^2=\frac{3}{2}x$

Answer 1

The correct option is C $y^2=\frac{9}{2}x$

The vertex of the parabola is $O(0,0)$ and tis axis lie along the x-axis.

So its equation is $y^2=4axor{y}^2=-4ax$

But it passes through the point $P(2,3)$ so its equation is $y^2=4ax$

since it passes through $P(2,3)$ we have $4a\times 2=9\Rightarrow a=\frac{9}{8}$

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