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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 (3, 4)
Solution
Vertex of the parabola is at the 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 (3, 4), it lies in 1st quadrant.
∴ Required parabola is y2 = 4ax.
Substituting x = 3 and y = 4 in y2 = 4ax, we get
(4)2 = 4a(3)
∴ a = `16/12 = 4/3`
∴ The required equation of the parabola is
y2 = `4(4/3)`x, i.e., y2 = `(16/3)`x, i.e., 3y2 = 16x.
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