Question

Which of the following is the equation of a circle with a radius of 2.5 and its center at (-4, 3)?

A. (x - 4)^2 + (y + 3)^2 = 2.5
B. (x + 4)^2 + (y - 3)^2 = 2.5
C. (x - 4)^2 + (y + 3)^2 = 6.25
D. (x + 4)^2 + (y -3)^2 = 6.25

Answer 1

The format for a circle is
`(x-h) ^(2) +(y-k) ^(2) = r^(2)`. We are given our center of (-4, 3) where h is -4 and k is 3. The radius of 2.5 will be squared to finish it off. Filling in our h and k accordingly gives us
`(x-(-4)) ^(2) +(y-3) ^(2) =6.25`. Clean that up a bit and we have
`(x+4) ^(2) +(y-3) ^(2) =6.25`, choice D above.