10. Consider the circles with the following equations:
1 answer:
Answer:
a) 5 and 10
b) 15
c) The center-to-center distance is the sum of the radii, so the circles must be tangent.
Step-by-step explanation:
a) Each equation is in standard form:
(x -h)^2 + (y -k)^2 = r^2
so the first circle has radius √25 = 5, and the second circle has radius √100 = 10. The radii of the circles are 5 and 10.
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b) The center-to-center distance can be found from the distance formula:
d = √((x2-x1)^2 +(y2-y1)^2) = √((9-0)^2 +(12-0)^2) = √(81 +144)
d = √225 = 15
The distance between centers if 15 units.
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c) The circles must be tangent because their center-to-center distance is the same as the sum of their radii.
5 + 10 = 15
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