Question

A circle has its center at (−1, 2) and a radius of 3 units. What is the equation of the circle?

(x − 1)2 + (y + 2)2 = 3
(x + 1)2 + (y − 2)2 = 3
(x + 1)2 + (y + 2)2 = 9
(x + 1)2 + (y − 2)2 = 9

Answer 1

standard equation of a circle
\[(x+a)^{2}+(y+b)^{2}=r^2\]

if we let
x+a=0
solve for x
x=-a

and

y+b=0
solve for y
y=-b

this means our centre is (-a, -b)

so if you had a centre (2,3) and a radius 5
then
x=2, so x-2=0
y=3, so y-3=0
you would substitute into the standard equation of a circle to get

\[(x-2)^{2}+(y-3)^{2}=5^{2}\]


so can you use these same steps to solve your question?