CPM Homework Help : CCA2 Problem 5-52

Complete the square (for $x$ ) to write the equation that follows in graphing form and sketch the graph of $x^2+y^2−4x−16=0$ . What is the parent graph and how has it been transformed?

Step 1:

Gather the $x$ terms together and move the constants to the right side of the equation.

$(x^2−4x+?)+y^2=16$

Step 2:

Determine what value will complete the square and add it to both sides of the equation.

$(x^2−4x+4)y^2=16+4$

Step 3:

Factor and identify the center of the circle and the radius.

$(x−2)^2+y^2=20$