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

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

by bhumika.k.shah » Fri Jan 22, 2010 12:43 pm
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. 3pie
B. 3 sqrt 2 pie
C. 3 sqrt 3 pie
D. 9pie
E. 18pie

OA E
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by ace_gre » Fri Jan 22, 2010 1:11 pm
Distance between (2,-3) and (5,0) is( (x1-x2)^2 + (y1-y2)^2)^1/2
Radius = ((2-5)^2 + (-3)^2)^1/2
==> (18)^1/2

Area of circle = pie r^2
==> 18 pie
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by bhumika.k.shah » Fri Jan 22, 2010 9:31 pm
Hi ,
i got the way you did the sum ....but whats d logic behind it ? if u could let me know that! :-)

Is there a formula for this ?
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by linkinpark » Fri Jan 22, 2010 9:35 pm
Bhumika
ace_gre wrote:( (x1-x2)^2 + (y1-y2)^2)^1/2
is the formula for finding distance between two points. we're told 2,-3 is center and that circle passes through other point. which means distance between center point and the other point is radius

formula for finding distance between (x,y) and (x1,y1) = square_root( (x-x1)^2 + (y-y1)^2 )
530->480->580
when posting a question don't post OA(even masked) before some discussion.
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by bhumika.k.shah » Fri Jan 22, 2010 9:45 pm
linkin is it sq rt (x-x1)^2 ... or ( (x1-x2)^2 + (y1-y2)^2)^1/2 ???

Can u gemme the exact formula ?

linkinpark wrote:Bhumika
ace_gre wrote:( (x1-x2)^2 + (y1-y2)^2)^1/2
is the formula for finding distance between two points. we're told 2,-3 is center and that circle passes through other point. which means distance between center point and the other point is radius

formula for finding distance between (x,y) and (x1,y1) = square_root( (x-x1)^2 + (y-y1)^2 )
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by thephoenix » Fri Jan 22, 2010 9:51 pm
bhumika.k.shah wrote:linkin is it sq rt (x-x1)^2 ... or ( (x1-x2)^2 + (y1-y2)^2)^1/2 ???

Can u gemme the exact formula ?

linkinpark wrote:Bhumika
ace_gre wrote:( (x1-x2)^2 + (y1-y2)^2)^1/2
is the formula for finding distance between two points. we're told 2,-3 is center and that circle passes through other point. which means distance between center point and the other point is radius

formula for finding distance between (x,y) and (x1,y1) = square_root( (x-x1)^2 + (y-y1)^2 )
the form is
dis b/n two points a(x1,y1)and b(x2,y2) is

sqrt[(x1-x2)^2+(y1-y2)^2]

here x1=2 ; y1=-3
and x2=5 ; y2=0

hence r=3 rut 2
and area is 18 * pie
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by Scott@TargetTestPrep » Fri May 22, 2015 4:59 am
bhumika.k.shah 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. 3pie
B. 3 sqrt 2 pie
C. 3 sqrt 3 pie
D. 9pie
E. 18pie

OA E
Solution:

Because the circle passes through point (5,0) and has center (2,-3), we know that the distance between these points is the radius of the circle.

Since we are given the coordinates for each point, the easiest thing to do is to use the distance formula to determine the circle's radius. The distance formula is:

Distance= √[(x2 - x1)^2 + (y2 - y1)^2]

We are given two ordered pairs, so we can label the following:

x1 = 2
x2 = 5

y1 = -3
y2 = 0

When we plug these values into the distance formula, we have:

Distance= √[(5 - 2)^2 + (0 - (-3))^2]

Distance= √ [(3)^2 + (3)^2]
Distance= √ [9 + 9]

Distance = √ [18]

Distance = √9 x √2

Distance = 3 x √2

Thus, we know that the radius = 3 x √2.

Finally, we can use the radius to determine the area of the circle.

area = πr^2

area = π(3 x √2 )^2

area = π(9 x 2 )

area = 18Ï€

The answer is E

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by vickysan » Wed Jun 03, 2015 9:24 pm
thephoenix wrote:
bhumika.k.shah wrote:linkin is it sq rt (x-x1)^2 ... or ( (x1-x2)^2 + (y1-y2)^2)^1/2 ???

Can u gemme the exact formula ?

linkinpark wrote:Bhumika
ace_gre wrote:( (x1-x2)^2 + (y1-y2)^2)^1/2
is the formula for finding distance between two points. we're told 2,-3 is center and that circle passes through other point. which means distance between center point and the other point is radius

formula for finding distance between (x,y) and (x1,y1) = square_root( (x-x1)^2 + (y-y1)^2 )
the form is
dis b/n two points a(x1,y1)and b(x2,y2) is

sqrt[(x1-x2)^2+(y1-y2)^2]

here x1=2 ; y1=-3
and x2=5 ; y2=0

hence r=3 rut 2
and area is 18 * pie
Thanks for the formula and the clear breakdown!
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by nikhilgmat31 » Thu Jun 04, 2015 8:46 pm
In simple terms radius of circle is distance between two points.

then do pie * radius^2
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