Question
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
∴ Equation of circle is x2 + y2 = 20.