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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 (1, –6)
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 (1, – 6), it lies in 4th quadrant
∴ Required parabola is y2 = 4ax
Substituting x = 1 and y = – 6 in y2 = 4ax, we get
(–6)2 = 4a(1)
∴ 36 = 4a
∴ a = `36/4` = 9
∴ The required equation of the parabola is
y2 = 4(9)x, i.e., y2 = 36x.
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