Question

A circle whose center is at (5, -3) and which passes through the point (7, -8) has a radius equal to

Answer 1

The distance from the center to any point on the circle is the radius.
Use the distance formula to find the radius:
d =
`\sqrt{(x_(2) - x_(1))^(2) + ( y_(2) - y_(1))^(2) }`
=
`\sqrt{(5 - 7)^(2) + (-3 + 8})^(2)}`
=
`\sqrt{(-2)^(2) + (5})^(2)}`
=
`√((4 + 25))`
=
`√(29)`

Answer: the radius of the circle is
`√(29)`