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Question: The vertex of the parabola y<sup>2</sup> = 8x is at the centre of a circle and the parabola cuts the...

The vertex of the parabola y2 = 8x is at the centre of a circle and the parabola cuts the circle at the ends of its latusrectum. Then the equation of the circle is

A

x2 + y2 = 4

B

x2 + y2 = 20

C

x2 + y2 = 80

D

x2 + y2 = 16

Answer

x2 + y2 = 20

Explanation

Solution

Centre of the circle = (0, 0) = 0.

L = one end of the latusrectum = (a, 2a) = (2, 4)

∴ radius of the circle = OL = 20\sqrt{20}

∴ Equation of circle is x2 + y2 = 20.