Question

Find the equation of circle of radius, $3$, passing through the origin and having its centre on the x-axis.

Answer 1

center of $x$ axis = $(x,0)$

and radius $=3$, passing through origin -

$\sqrt{(x-0{)}^2+(0-0{)}^2}=3$

$x^2=9$

$x=\pm 3$

$\therefore$ center $=(3,0)$ or $(-3,0)$

$\therefore$ equation of circle is

${(x-3)}^2+y^2=3^2\Rightarrow x^2+y^2{y}^2-6x=0$

or

$(x+3{)}^2+y^2=3^2\Rightarrow x^2+y^2+6x=0$