Question

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$passing through $(2, 3)$and the axis is along the x-axis

Answer 1

_Given that _

vertex is $(0, 0)$and the axis of the parabola is the x-axis,

then the equation of the parabola is either of the forms $y^2= 4ax$ or $y^2= -4ax.$
The parabola passes through the point $(2, 3),$ which lies in the first quadrant.
Therefore, the equation of the parabola is of the form $y^2= 4ax$

, while points $(2, 3)$ must satisfy the equation $y^2= 4ax.$

$∴ 3^2 = 4a(2)$

$3^2 = 8a$

$9 = 8a$

$a = \dfrac{9}{8}$
Thus, the equation of the parabola is

$y^2 = 4 (\dfrac{9}{8})x$

$⇒y^2=\dfrac{9x}{2}$

$⇒2y^2 = 9x$

∴ The equation of the parabola is $2y^2 = 9x.$ (Ans)