Thread: Circle Graphs

For each question below, there is a circle given in the textbook with information. I will explain with words what each graph displays in the book.

Instructions for BOTH circles:

(a) Find the center and radius of each circle.

(b) Write the standard form of the equation of each circle?

CIRCLE A PICTURE HAS:

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

CIRCLE B PICTURE HAS:

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

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 can see that 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.

My guess is that these two points are the ends of a diameter.

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.

This is exactly what I was looking for in terms of an answer.

Yes, each point on the graph lies on the circle at the end of a diameter.