Question

Center: (-10, -4), Point on Circle: (4, -2)

Use the information given to write an equation of the vircle.

Answer 1

Explanation:

Left hand side.

The left hand side is the general equation that includes the center of the circle.

The center is at -10,-4

(x + 10)^2 + (y + 4)^2 = r^2

Finding the radius.

the radius is found from the given point on the circle

Givens

x1 = -10

x2 = 4

y1 = - 4

y2 = - 2

Equation

r^2 = (y2 - y1)^2 + (x2 - x1)

r^2 = (-2 - - 4)^2 + (4 - - 10)^2

r^2 = 2^2 + 14^2

r^2 = 200

Note:

• The graph below shows two things: the first is that the center is at -10,-4
• The second is that the radius is a little more than 14. The equation of a circle always expresses the radius as r^2