+0

0
433
3
+4690

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

May 26, 2017

#1
+7348
+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

May 26, 2017

#1
+7348
+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
#2
+74
+2

Well done.

RosyWintercat  May 26, 2017
#3
+4690
+2

Thank you! :)

NotSoSmart  May 26, 2017