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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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New post 29 Mar 2020, 08:42
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A
B
C
D
E

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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New post 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.

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

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

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