Question

Use the given information to write the standard equation of the circle.

Answer 1

well, we know its center and a point on the circle, well, the distance from the center to a point on it is well, you guessed it!! is its radius.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-7}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-8})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{ radius }{r}=√((~~1 - (-7)~~)^2 + (~~-8 - (-2)~~)^2) \implies r=√((1 +7)^2 + (-8 +2)^2) \\\\\\ r=√(( 8 )^2 + ( -6 )^2) \implies r=√( 64 + 36 ) \implies r=√( 100 )\implies r=10 \\\\[-0.35em] ~\dotfill`

`\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-7}{h}~~,~~\underset{-2}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-7) ~~ )^2 ~~ + ~~ ( ~~ y-(-2) ~~ )^2~~ = ~~10^2\implies (x+7)^2 + (y+2)^2 = 100`