Question

A circle has center (1,3) and passes through (4,-1) How do you use the distance formula to find the length of the radius of the circle?

Answer 1

By definition the radius of a circle is the distance between the center and any point on the circumference of the circle.

Explanation:

If a circle has
`color(white)("XXX")`center at `(1,3)`
and
`color(white)("XXX")(4,1)` is a point on the circumference.

The radius of the circle is
`color(white)("XXxX")r=sqrt((1-4)^2+(3-1)^2)`

`color(white)("XXxX")=sqrt(3^2+2^2)`

`color(white)("XXxX")=sqrt(13)`