Which of the following circles have their centers in the second quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x + 3)2 + (y - 2)2 = 8C.(x + 12)2 + (y - 9)2 = 19D.(x - 2)2 + (y + 7)2 = 64SUBMITarrow_backPREVIOUS
Question
Which of the following circles have their centers in the second quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x + 3)2 + (y - 2)2 = 8C.(x + 12)2 + (y - 9)2 = 19D.(x - 2)2 + (y + 7)2 = 64SUBMITarrow_backPREVIOUS
Solution
The equation of a circle in a coordinate plane is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
The second quadrant is the area where x is negative and y is positive.
Let's check each option:
A. (x - 5)² + (y + 5)² = 9 The center of this circle is at (5, -5), which is in the fourth quadrant, not the second.
B. (x + 3)² + (y - 2)² = 8 The center of this circle is at (-3, 2), which is in the second quadrant.
C. (x + 12)² + (y - 9)² = 19 The center of this circle is at (-12, 9), which is in the second quadrant.
D. (x - 2)² + (y + 7)² = 64 The center of this circle is at (2, -7), which is in the fourth quadrant, not the second.
So, the circles B and C have their centers in the second quadrant.
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