Raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). label the center and at least four points on the circle. write the equation of the circle.

Equation:

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

Plug in the points to get:

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

The equation of the circle is given by:

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

We expand to get:

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

The point (5,0) and (-7,0) lies on the circle.

When x=0

The point (0,-5) and (0,7) lie on this circle.