Find the equation of a parabola with vertex at the origin, the axis along the x - axis and passing through (2, 3).
Given that we need to find the equation of the parabola whose vertex is at origin and axis along the x - axis and also passing through (2, 3).
We know that the standard equation of the parabola whose axis is x - axis and vertex at origin is y2 = 4ax.
Substituting (2, 3) in the equation of parabola.
⇒ (3)2 = 4a(2)
⇒ 9 = 8a
⇒ 
Now,
⇒ 
⇒ 
⇒ 2y2 = 9x.
∴The equation of the parabola is 2y2 = 9x.
9