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
  1. $x^2+y^2+4 x-6 y-9=0$
  2. $x^2+y^2+4 x-6 y+9=0$
  3. $x^2+y^2+4 x-6 y-3=0$
  4. $x^2+y^2-4 x+6 y-9=0$

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 $(x+2)^2+(y-3)^2=4$ $\therefore \quad x^2+y^2+4 x-6 y+9=0$

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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