#1**+3 **

a.

The center of the circle will be the midpoint of the diameter's endpoints.

midpoint = ( average of the x's , average of the y's )

midpoint = ( \(\frac{-10+4}{2} , \frac{-2+6}{2}\) )

midpoint = ( -3 , 2 )

b.

The radius will be the distance from the midpoint to an endpoint of the diameter. We can use the distance formula to find this distance.

radius = \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

radius = \(\sqrt{(-3-(-10))^2+(2-(-2))^2}\)

radius = \(\sqrt{49+16}\)

radius = \(\sqrt{65}\)

c.

The equation of a circle is (x - h)^{2} + (y - k)^{2} = r^{2}

Where ( h, k ) is the center point, and r is the radius.

Just plug in the center point and radius into the equation.

(x + 3)^{2} + (y - 2)^{2} = 65

hectictar
Apr 11, 2017