Question

Points F(2,6) and G(14,22) are the endpoints of a diameter of circle M. What is the equation of circle M?

Answer 1

`(x - 8)^(2) + (y - 14)^(2) = 100`

Explanation:

The equation of a circle has the following format:

`(x - x_(0))^(2) + (y - y_(0))^(2) = r^(2)`

In which r is the radius(half the diameter) and the centre is the point
`(x_(0), y_(0))`

Radius:

The radius is half the diameter.

The diameter is the distance between the two end points(F and G). So

`D = \sqrt{(14-2)^(2) + (22-6)^(2)} = 20`

So

`r = (D)/(2) = (20)/(2) = 10`

Centre:

Halfway point between f and g. So

`x_(0) = (2+14)/(2) = 8`

`y_(0) = (6+22)/(2) = 14`

What is the equation of circle M?

`(x - 8)^(2) + (y - 14)^(2) = 100`