Question

Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.

Answer 1

Start moving constants to the other side of the equation,

`x^2+y^2-8x+2y=-13`

group the x-stuff and y-stuff together,

`x^2-8x+y^2+2y=-13`

multiply by 1/2 the x-term and the y-term in order to find the missing number in order to complete the squares,

`\begin{gathered} -8\ast(1)/(2)=-4 \\ 2\ast(1)/(2)=1 \end{gathered}`

add both terms squared on both sides

`(x^2-8x+(-4)^2)+(y^2+2y+(1)^2)=-13+(-4)^2+1^2`

simplify and write as the squared form,

`(x-4)^2+(y+1)^2=4`

The center of the circle is at (4,-1) and has a radius of 2