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Help asap thanks please!

what is the equation of the circle with center (-6,7) that passes through the poing (4,-2) ?

NotSoSmart  May 26, 2017

Best Answer 

 #1
avatar+7324 
+2

We need to find the distance between (-6, 7) and (4, -2) . That distance is the radius of this circle.

 

distance  \(=\sqrt{[(-6)-(4)]^2+[(7)-(-2)]^2} \\~\\ =\sqrt{[10]^2+[9]^2} \\~\\ =\sqrt{100+81} \\~\\=\sqrt{181}\)

 

So...the radius of this circle is \( \sqrt{181} \) , and the center of this circle is (-6, 7) .

This makes the equation:

 

( y - 7 )2 + ( x - (-6) )2   =   ( \( \sqrt{181} \)  )2

 

( y - 7 )2 + ( x + 6 )2   =   181

hectictar  May 26, 2017
 #1
avatar+7324 
+2
Best Answer

We need to find the distance between (-6, 7) and (4, -2) . That distance is the radius of this circle.

 

distance  \(=\sqrt{[(-6)-(4)]^2+[(7)-(-2)]^2} \\~\\ =\sqrt{[10]^2+[9]^2} \\~\\ =\sqrt{100+81} \\~\\=\sqrt{181}\)

 

So...the radius of this circle is \( \sqrt{181} \) , and the center of this circle is (-6, 7) .

This makes the equation:

 

( y - 7 )2 + ( x - (-6) )2   =   ( \( \sqrt{181} \)  )2

 

( y - 7 )2 + ( x + 6 )2   =   181

hectictar  May 26, 2017
 #2
avatar+74 
+2

Well done.

RosyWintercat  May 26, 2017
 #3
avatar+3486 
+2

Thank you! :)

NotSoSmart  May 26, 2017

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