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

Answer:

$(x - 8)^{2} + (y - 14)^{2} = 100$

Step-by-step 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

$r = \frac{D}{2} = \frac{20}{2} = 10$

Centre:

Halfway point between f and g. So

$x_{0} = \frac{2+14}{2} = 8$

$y_{0} = \frac{6+22}{2} = 14$

What is the equation of circle M?

$(x - 8)^{2} + (y - 14)^{2} = 100$