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Question
Find the equation of the parabola that satisfies the following condition:
Vertex (0, 0) passing through (2, 3) and axis is along x-axis
Solution
Since the vertex is (0, 0) and the axis of the parabola is the x-axis, the equation of the parabola is either of the form y2 = 4ax or y2 = –4ax.
The parabola passes through point (2, 3), which lies in the first quadrant.
Therefore, the equation of the parabola is of the form y2 = 4ax, while point
(2, 3) must satisfy the equation y2 = 4ax.
∴ 32 = 4a (2) or a = `9/8`
Thus, the equation of the parabola is
y2 = `4(9/8)x`
y2 = `9/8x`
2y2 = 9x
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