Question

A circle passes through the point (2,2) and has its center at (1,-3). The radius of the circle is _ units.

Answer 1

radius =
`√(26)` units

Explanation:

The radius r is the distance from the centre to a point on the circle.

Using the distance formula to calculate r

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (1, - 3)

r =
`√((1-2)^2+(-3-2)^2)`

=
`√((-1)^2+(-5)^2)`

=
`√(1+25)`

=
`√(26)`