# Circle Graphs

• Jan 14th 2007, 05:23 AM
symmetry
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.
• Jan 14th 2007, 06:19 AM
Soroban
Hello, symmetry!

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

Given: center \$\displaystyle (h,k)\$ and radius \$\displaystyle r\$
. . . . . the equation is: .\$\displaystyle (x-h)^2 + (h - k)^2\:=\:r^2\$

Quote:

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: .\$\displaystyle (h,k) = (1,2)\$

The radius is the distance from the center \$\displaystyle (1,2)\$ to the point \$\displaystyle (1,0)\$.
. . You can see that the distance is \$\displaystyle 2\$, right?

Write the equation: .\$\displaystyle (x-1)^2 + (y-2)^2\:=\:2^2\$

Quote:

[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 \$\displaystyle M\$ between the two points.
. . Use the Midpoint Formula to find it.

Then use the Distance Formula to find the distance from \$\displaystyle M\$ to one of the points.
. . That, of course, is the radius.

• Jan 14th 2007, 06:26 AM
symmetry
ok
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.