Question

A circle has a center at the origin and the point (3,4) is on the circle

Answer 1

Answer: 5 units

Explanation:

The standard form of equation of circle:

`(x-h)^2+(y-k)^2=r^2` , where (h,k) = center of circle, r= radius.

Given : Center of circle= origin = (0,0) =(h,k)

Point on circle = (3,4)

Put x= 3 , y=4 , h=0 , k=0 , then the equation will become

`(3-0)^2+(4-0)^2=r^2\\\\\Rightarrow\ 9+16=r^2\\\\\Rightarrow\ 25=r^2\\\\\Rightarrow\ r=5`

Hence, the radius is 5 units long.