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In the coordinate plane, a circle has center (2, -3) and

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In the coordinate plane, a circle has center (2, -3) and  [#permalink]

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New post 27 Feb 2018, 02:55
Bunuel wrote:
GMATD11 wrote:
zaarathelab wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π


Can any body draw the picture for this

i thought y coordinate between (5,0) & (2,-3) will be radius i.e 3
and area will be 3*3pie


The point is that the radius does not equal to 3, it equals to \(3\sqrt{2}\). You can find the length of the radius either with the distance formula (the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)) or with Pythagoras theorem. Look at the diagram below:

Image

The radius of the circle is the hypotenuse of a right isosceles triangle with the legs equal to 3: \(r^2=3^2+3^2=18\) --> \(area=\pi{r^2}=18\pi\).

Answer: E.

Hope it helps.

Attachment:
graph.png



Bunuel shouldnt i convert 18 to \(3\sqrt{2}\) ? :? if not why ?

And what do you mean by " The point is that the radius does not equal to 3, it equals to \(3\sqrt{2}\) " how did find out that radius is \(3\sqrt{2}\) :?
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Re: In the coordinate plane, a circle has center (2, -3) and  [#permalink]

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New post 27 Feb 2018, 04:41
1
dave13 wrote:
Bunuel wrote:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3π
B. 3√2π
C. 3√3π
D. 9π
E. 18π

The point is that the radius does not equal to 3, it equals to \(3\sqrt{2}\). You can find the length of the radius either with the distance formula (the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)) or with Pythagoras theorem. Look at the diagram below:

Image

The radius of the circle is the hypotenuse of a right isosceles triangle with the legs equal to 3: \(r^2=3^2+3^2=18\) --> \(area=\pi{r^2}=18\pi\).

Answer: E.

Hope it helps.

Attachment:
graph.png



Bunuel shouldnt i convert 18 to \(3\sqrt{2}\) ? :? if not why ?

And what do you mean by " The point is that the radius does not equal to 3, it equals to \(3\sqrt{2}\) " how did find out that radius is \(3\sqrt{2}\) :?


1. We got that r^2 =18. The formula for the area is \(area=\pi{r^2}\). So, we can directly plug there the value of r^2 without finding the value of r.

2. r^2 =18 = 9*2--> \(r=3\sqrt{2}\)
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Re: In the coordinate plane, a circle has center (2, -3) and &nbs [#permalink] 27 Feb 2018, 04:41

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