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For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are

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Bunuel
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For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   27 May 2019, 01:46
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For the circle \((x-1)^2 + (y+1)^2 = 20\) in the xy-plane, what is the area of the circle ?

A. \(10 \pi\)
B. \(16 \pi\)
C. \(18 \pi\)
D. \(20 \pi\)
E. \(25 \pi\)
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D
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   27 May 2019, 02:06
Bunuel wrote:
For the circle \((x-1)^2 + (y+1)^2 = 20\) in the xy-plane, what is the area of the circle ?

A. \(10 \pi\)
B. \(16 \pi\)
C. \(18 \pi\)
D. \(20 \pi\)
E. \(25 \pi\)


Equation of circle is \((x-a)^2\) + \((y-b)^2\) = \(r^2\)

So, \(r^2\) = 20

Area of circle = \(\pi\)\(r^2\) = 20\(\pi\)

Option D
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   27 May 2019, 05:21
Bunuel wrote:
For the circle \((x-1)^2 + (y+1)^2 = 20\) in the xy-plane, what is the area of the circle ?

A. \(10 \pi\)
B. \(16 \pi\)
C. \(18 \pi\)
D. \(20 \pi\)
E. \(25 \pi\)


eqn of circle ;
x^2+y^2=r^2
r^2=20
so
area pi*r^2
pi*20
IMO D
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nissstheone
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   13 Jun 2019, 02:15
can someone please explain = Equation of circle is (x−a)2(x−a)2 + (y−b)2(y−b)2 = r2 ??
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Bunuel
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   13 Jun 2019, 02:36
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nissstheone wrote:
can someone please explain = Equation of circle is (x−a)2(x−a)2 + (y−b)2(y−b)2 = r2 ??




This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b.

If the circle is centered at the origin (0, 0), then the equation simplifies to: \(x^2+y^2=r^2\).

For more on this subject check Coordinate Geometry chapter of Math Book: https://gmatclub.com/forum/math-coordina ... 87652.html
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   05 Jul 2019, 19:20
Hello Bunuel, how did you establish that the circle in given problem is centered at origin, as the same is not stated in the problem statement. Also, the equation x^2+Y^2=R^2 is true only for circles with center as origin, isn't it?

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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink] New post   19 Jul 2019, 10:53
omkartadsare wrote:
Hello Bunuel, how did you establish that the circle in given problem is centered at origin, as the same is not stated in the problem statement. Also, the equation x^2+Y^2=R^2 is true only for circles with center as origin, isn't it?

Posted from my mobile device


Yes, I too was thinking about the same point
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Re: For the circle (x-1)^2 + (y+1)^2 = 20 in the xy-plane, what is the are [#permalink]
19 Jul 2019, 10:53
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