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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?

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

$(x^2−4x+?)+y^2=16$

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

$(x^2−4x+4)y^2=16+4$

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

$(x−2)^2+y^2=20$