Question

Which of the following circles have their centers in the second quadrant? Check all that apply.

Answer 1

The given circles are given in standard form:
(x - xc)² + (y - yc)² = r²

The second quadrant is the one that has negative x coordinates and positive y coordinates.

This said, let's see all your options:
A) (x - 5)² + (y - 6)² = 25
xc = -(-5) = +5
yc = -(-6) = +6
C (5 , 6) is in the first quadrant.

B) (x + 1)² + (y - 7)² = 16
xc = -(+1) = -1
yc = -(-7) = +7
C (-1 , 7) is in the second quadrant.

C) (x - 4)² + (y + 3)² = 32
xc = -(-4) = +4
yc = -(+3) = -3
C (4, -3) is in the fourth quadrant.

D) (x + 2)² + (y - 5)²= 9
xc = -(+2) = -2
yc = -(-5) = +5
C (-2 , +5) is in the second quadrant.

Therefore, the correct answers are B and D.