what is the equation of the circle with Center (-6, 7) that passes through the point (4, -2) ​

Question

what is the equation of the circle with Center (-6, 7) that passes through the point (4, -2) ​

in progress 0
Emery 5 days 2021-10-13T03:39:52+00:00 1 Answer 0

Answers ( )

  1. Charlotte
    0
    2021-10-13T03:41:08+00:00

    we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.

    \bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill

    \bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )