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Question
Find the equation of the parabola that satisfies the following condition:
Vertex (0, 0); focus (3, 0)
Solution
Vertex (0, 0); focus (3, 0)
Since the vertex of the parabola is (0, 0) and the focus lies on the positive x-axis, x-axis is the axis of the parabola, while the equation of the parabola is of the form y2 = 4ax.
Since the focus is (3, 0), a = 3.
Thus, the equation of the parabola is y2 = 4 × 3 × x, i.e., y2 = 12x
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