Question

A circle has its centre 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. $x^2+y^2=2$

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 $(-2,1).$
$\therefore$ Centre of the circle is $(0,0)$ and radius of the circle is
$\sqrt{(2-0{)}^2+(1-0{)}^2}=\sqrt{5}$
$\therefore$ Equation of circle is
$(x-0{)}^2+(y-0{)}^2=(\sqrt{5}{)}^2$
$x^2+y^2=5$