Q. 265.0( 2 Votes )

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

Answer :

Since the parabola is symmetric about x-axis and has its vertex at the origin, the equation is of the form y

^{2}= 4ax or y

^{2}= -4ax, where the sign depends on whether the parabola opens to the right or left. But the parabola passes through (2, 3) which lies in the first quadrant, it must open to the right. Thus the equation is of the form y

^{2}= 4ax.

Since the parabola passes through (2, 3) we have

3^{2} = 4a(2) ⇒ 9 = 8a ⇒ a =

Therefore, the equation of the parabola is

y^{2} = 4 = x ⇒ 2y^{2} = 9x.

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