5.0k views
5 votes
Points F(2,6) and G(14,22) are the endpoints of a diameter of circle M. What is the equation of circle M?

1 Answer

0 votes

Answer:


(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

User Hrqls
by
6.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.