Find the equation of the parabola that satisf | vedclass

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(A) Since the vertex is $(0, 0)$ and the axis of the parabola is the $x$-axis,the equation of the parabola is of the form $y^2 = 4ax$.The parabola pas

Vedclass · Accepted Answer

$2y^2 = 9x$

Vedclass · Answer

(A) Since the vertex is $(0, 0)$ and the axis of the parabola is the $x$-axis,the equation of the parabola is of the form $y^2 = 4ax$.The parabola passes through the point $(2, 3)$,which lies in the first quadrant.Substituting the point $(2, 3)$ into the equation $y^2 = 4ax$:$3^2 = 4a(2)$$9 = 8a$$a = \frac{9}{8}$Thus,the equation of the parabola is:$y^2 = 4 \left( \frac{9}{8} \right) x$$y^2 = \frac{9}{2} x$$2y^2 = 9x$

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.

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