ParabolaHard

Question

From the focus of the parabola y2 = 8x as centre, a circle is described so that a common chord of the curves is equidistant from the vertex and focus of the parabola. The equation of the circle is -

Options

A.(x - 2)2 + y2 = 3
B.(x - 2)2 + y2 = 9
C.(x + 2)2 + y2 = 9
D.x2 + y2 - 4x = 0

Solution

     
Focus of parabola y2 = 8x is (2, 0). Equation of circle with centre (2, 0) is
(x - 2)2 + y2 = r2
AB is common chord
Q is mid point i.e. (1, 0)
AQ2 = y2 where y2 = 8 × 1 = 8
∴   r2 = AQ2 + QS2 = 8 + 1 = 9
so circle is (x - 2)2 + y2 = 9

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