The equation of a circle with center at $(-2,3)$ and circumference of $4 \pi$ units is
The equation of a circle with center at $(-2,3)$ and circumference of $4 \pi$ units is
$x^2+y^2+4 x-6 y-9=0$
$x^2+y^2+4 x-6 y+9=0$
$x^2+y^2+4 x-6 y-3=0$
$x^2+y^2-4 x+6 y-9=0$
Solution
Circumference of circle is $4 \pi$.
$\therefore \quad 2 \pi r=4 \pi ; \therefore r=2$
Equation of circle whose centre is $(-2,3)$ and radius 2 is
$(x+2)^2+(y-3)^2=4$
$\therefore \quad x^2+y^2+4 x-6 y+9=0$