Question

lf $(-2,5)$ is the centre of the circle which touches $y$-axis, then the equation of the circle is

• A. $x^2+y^2-4x-10y+25=0$
• B. $x^2+y^2-4x-10y+4=0$
• C. $x^2+y^2+4x+10y+2=0$
• D. $x^2+y^2+4x-10y+25=0$

Answer 1

Answer: (D)

$x^2+y^2+4x-10y+25=0$

If the circle touches Y- axis , then its x- coordinate has magnitude equal to radius $\left(r\right)$.
$\therefore$ centre of circle is $(-2,5)$.
then , $r=2$
$\therefore$ equation of circle is
$(x+2{)}^2+(y-5{)}^2=4$
$\Rightarrow x^2+y^2+4x-10y+25=0$