Hello, symmetry!

You're expected to know the general equation of a circle.

Given: center and radius

. . . . . the equation is: .

Find the center and radius of each circle.

Write the standard form of the equation of each circle.

[1] CIRCLE A PICTURE HAS:

Point (1, 0) on the circle and point (1, 2) in what appears to be the center of the circle.

You already know the center: .

The radius is the distance from the center to the point .

. . You canseethat the distance is , right?

Write the equation: .

[2] CIRCLE B PICTURE HAS:

Point (0, 1) on the circle and point (2, 3) also on the circle.

There is not enough information to determine a specific circle.

Myguessis that these two points are the ends of adiameter.

If that's true, the center is the midpoint between the two points.

. . Use the Midpoint Formula to find it.

Then use the Distance Formula to find the distance from to one of the points.

. . That, of course, is the radius.