Part 2: Identify the center and radius of each. Then sketch the graph.

1. x^2 + y^2 - 4x + 6y + 9 = 0

2. x^2 + y^2 + 6x + 2y + 9 = 0

3. x^2 + y^2 - 6x + 2y + 1 = 0

4. x^2 + y^2 - 8x -2y + 8 = 0

See below for graphs

Step-by-step explanation:

I like to solve a set of problems like this once, then use a calculator or spreadsheet to crunch the numbers.

We can start with the general form of the equation for a circle:

  x^2 +y^2 +ax +by +c = 0

Completing the square gives ...

  (x^2 +ax +(a/2)^2) +(y^2 +by +(b/2)^2) = (a/2)^2 +(b/2)^2 -c

  (x +(a/2))^2 +(y +(b/2))^2 = (a/2)^2 +(b/2)^2 -c

Comparing this to the standard form formula ...

  (x -h)^2 + (y -k)^2 = r^2

we see the relations are ...

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

Then your circle centers and radii are ...

hint: which coefficient is a multiple of 360°?

step-by-step explanation: