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

#1**+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**+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