Question

Which of the following answer choices is an equation for the circle with a center of (-2, 3) and a radius of 3?

Answer 1

We have that the formula for the circle with a center of (-2, 3) and a radius of 3 is given by the formula:

$(x-(-2))^2+(y-3)^2=3^2=(x+2)^2+(y-3)^2=9$

Then, we can expand the previous expression as follows:

$x^2+4x+4+y^2-6y+9=9$

Thus

$x^2+4x+4+y^2-6y+9-9=0\Rightarrow x^2+4x+4+y^2-6y=0$

Therefore

$x^2+y^2+4x-6y+4=0$

Then, the correct answer is option D.