Which of the following circles have their centers on the y-axis?Check all that apply.A.(x - 0)2 + (y + 5)2 = 74B.(x - 0)2 + (y - 0)2 = 44C.(x - 4)2 + (y - 0)2 = 22D.(x + 1)2 + (y - 7)2 = 16SUBMITarrow_backPREVIOUS
Question
Which of the following circles have their centers on the y-axis?Check all that apply.A.(x - 0)2 + (y + 5)2 = 74B.(x - 0)2 + (y - 0)2 = 44C.(x - 4)2 + (y - 0)2 = 22D.(x + 1)2 + (y - 7)2 = 16SUBMITarrow_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. If a circle's center lies on the y-axis, then the x-coordinate of the center (h) must be 0.
Let's check each option:
A. (x - 0)² + (y + 5)² = 74 The center of this circle is at (0, -5), which lies on the y-axis.
B. (x - 0)² + (y - 0)² = 44 The center of this circle is at (0, 0), which lies on the y-axis.
C. (x - 4)² + (y - 0)² = 22 The center of this circle is at (4, 0), which does not lie on the y-axis.
D. (x + 1)² + (y - 7)² = 16 The center of this circle is at (-1, 7), which does not lie on the y-axis.
So, the circles in options A and B have their centers on the y-axis.
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