Question

Which of the following points lies on the circle whose center is at the origin and whose radius is 13?

(-5, 12)
W13, 13)
(6.-7)

Answer 1

any point that is on the circle will have a distance of "radius" units, namely 13 units, since the radius is just that.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{12})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√((-5-0)^2+(12-0)^2)\implies d=√((-5)^2+12^2) \\\\\\ d=√(25+144)\implies d=√(169)\implies d=13`