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Question
Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (2, 3)
Solution
Vertex of the parabola is at origin (0, 0) and its axis is along X-axis.
∴ Equation of the parabola can be either y2 = 4ax or y2 = –4ax.
Since the parabola passes through (2, 3), it lies in 1st quadrant.
∴ Required parabola is y2 = 4ax
Substituting x = 2 and y = 3 in y2 = 4ax, we get
(3)2 = 4a(2)
∴ 9 = 8a
∴ a = `9/8`
∴ The required equation of the parabola is
y2 = `4(9/8)`x, i.e., y2 = `9/2`x, i.e., 2y2 = 9x.
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