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Question 623803: The equations of three distinct circles are listed below. Using complete sentences, explain which of the three circles would intersect the x-axis only. Justify your answer.
Circle A: (x – 9)2 + (y – 3)2 = 25
Circle B: (x –7)2 + (y + 2)2 = 49
Circle C: (x + 2)2 + y2 = 16
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Circle A
Its center is (9, 3) and its radius is 5. Since the center is 9 units to the right of the y axis and the radius is only 5 units, this circle is not big enough to reach the y axis from (9, 3). So it will not intersect the y axis. But the center is only 3 units away from the x axis. So with a radius of 5 it will intersect the x axis.
Circle B
Its center is (7, -2) and its radius is 7. Since the center is 7 units to the right of the y axis and the radius is 7 units, this circle will just barely reach the y axis. In fact it will be tangent to it. IOW, it will intersect the y axis at just one point (0, -2). The center is only 2 units away from the x axis. So with a radius of 7 it will intersect the x axis.
Circle C
Its center is (-2, 0) and its radius is 4. Since the center is 2 units to the left of the y axis and the radius is 4 units, this circle will intersect the y axis (twice). The center is on the x axis. So the circle will definitely intersect the x axis (at (2, 0) and (-6, 0)).
In summary, only circle A would intersect just the x axis and not the y axis.
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