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# On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies

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On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies  [#permalink]

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29 Mar 2020, 08:42
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Difficulty:

25% (medium)

Question Stats:

88% (01:24) correct 13% (01:53) wrong based on 32 sessions

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On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies along the circle’s circumference. What is the square-unit area of the circle?

(A) $$36π$$

(B) $$\frac{81π}{2}$$

(C) $$41π$$

(D) $$48π$$

(E) $$57π$$

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Re: On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies  [#permalink]

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29 Mar 2020, 11:24

Solution

Given
In this question, we are given that
• On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies along the circle’s circumference

To find
We need to determine
• The square-unit area of the circle

Approach and Working out
The radius of the circle r = the distance between (2, -1) and (-3, 3) = $$\sqrt{5^2 + 4^2} = \sqrt{41}$$
• Hence, $$r^2 = 41$$
• Therefore, area of the circle = $$πr^2 = 41π$$

Thus, option C is the correct answer.

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Re: On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies  [#permalink]

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29 Mar 2020, 20:20
radius of the circle = distance b/w (2,-1) and (-3,3) = $$\sqrt{{41}}$$

so the area of the circle =$$\pi$$$$r^2$$ = 41$$\pi$$

Option C.
Re: On the xy-plane, a circle has center (2,-1), and the point (-3,3) lies   [#permalink] 29 Mar 2020, 20:20