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
[tex] \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 [/tex]
The length of the radius of a circle whose center is at the origin and passes through (3,4) will be 5.
A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x – h)² + (y – k)² = r²
We have (h, k) is (0, 0).
Then the equation will be
x² + y² = r²
The circle is passing through (3, 4), then we have
r² = 3² + 4²
r² = 9 + 16
r² = 25
r = 5
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