Question

Find the length of the radius of a circle whose center is at the origin and passes through (3,4)

Answer 1

well, by definition the distance from the center to a point on the circle is the radius. Well, we know the center is at 0,0 and a point is at 3,4, so

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(3-0)^2+(4-0)^2}\implies r=\sqrt{3^2+4^2} \\\\\\ r=\sqrt{9+16}\implies r=\sqrt{25}\implies r=5$