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In the xy-plane, a circle is centered at the point (-4,3) and passes

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Bunuel
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In the xy-plane, a circle is centered at the point (-4,3) and passes [#permalink] New post   15 May 2018, 02:29
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A
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E

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In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π
B. 12π
C. 16π
D. 20π
E. 25π
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E
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Re: In the xy-plane, a circle is centered at the point (-4,3) and passes [#permalink] New post   15 May 2018, 03:18
As the circle centered at (-4,3) passes from the origin. The distance between the center and the origin must be the radius

Therefore, using distance formula

\(= \sqrt{(-4^2 - 0^2) + (3^2 - 0^2)}\)
\(= \sqrt{25}\)
\(= 5\)

As radius is 5, area of circle is 25π

Answer is E
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Re: In the xy-plane, a circle is centered at the point (-4,3) and passes [#permalink] New post   15 May 2018, 04:05
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Solution



Given:
• In the x-y plane, a circle is centered at (-4, 3) and passes through the origin (0, 0)

To find:
• The area of the circle

Approach and Working:
• As the circle passes through (0, 0), this point is on the circumference of the circle
• Therefore, the distance between this point and the center indicates the length of the radius of the circle
    o Radius = \(\sqrt{{(-4 – 0)^2 + (3 – 0)^2}} = 5\) units
• So, the area of the circle = \(π * 5^2 = 25\) sq. units

Hence, the correct answer is option E.

Answer: E
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Re: In the xy-plane, a circle is centered at the point (-4,3) and passes [#permalink] New post   16 May 2018, 10:47
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Bunuel wrote:
In the xy-plane, a circle is centered at the point (-4,3) and passes through the origin. What is the area of the circle?

A. 9π
B. 12π
C. 16π
D. 20π
E. 25π


Since the circle is centered at the point (-4,3) and passes through the origin, we see that the radius is the hypotenuse of a triangle, with sides of 3 and 4, so we have a 3-4-5 right triangle with a hypotenuse of 5, which means the radius of the circle is also 5.

Thus, the area of the circle is π(5^2) = 25π,

Answer: E
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Re: In the xy-plane, a circle is centered at the point (-4,3) and passes [#permalink]
16 May 2018, 10:47
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