Question

A circle has its center at the vertex of the parabola $x^2=4y$ and the circle cuts the parabola at the ends of its latus rectum. The equation of the circle is

• A. $x^2+y^2=5$
• B. $x^2+y^2=4$
• C. $x^2+y^2=1$
• D. None of these

Answer 1

The correct option is A $x^2+y^2=5$

Coordinates of the vertex of the parabola $x^2=4y$ are $(0,0)$ and the ends of latus rectum are $(2,1)$ and $(-2,1)$

$\therefore$ Center of the circle is $(0,0)$ and radius of the circle is $=\sqrt{{\left(2\right)}^2+{\left(1\right)}^2}=\sqrt{5}$

$\therefore$ Equation of circle is $x^2+y^2=5$.