Question

The vertex of the parabola $y^2=8x$ is at the centre of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is

• A. $x^2+y^2=4$
• B. $x^2+y^2=20$
• C. $x^2+y^2=80$
• D. none of these

Answer 1

The correct option is B $x^2+y^2=20$

Vertex of the given parabola is $(0,0)$
and coordinates of the latus rectum $(a,2a)$ and $(a,-2a)$ Here ($a=2)$
so radius of the required circle is $r=\sqrt{a^2+4a^2}=\sqrt{20}$
Hence equation of circle is $x^2+y^2=r^2=20$