Question

Using the following equation, find the center and radius of the circle by completing the square.

x2 + y2 − 10x − 14y − 7 = 0

center: (−5, −7), r = 81
center: (−5, −7) r = 9
center: (5, 7), r = 81
center: (5, 7), r = 9

Answer 1

What ideas do you have from this?

Answer 2

start with the x terms

x^2 − 10x

the first step to completing the square is to take the coefficient of the x term (not the x^2 term, the x term), divide by 2, and square the result

so (-10/2)^2 = 25

add this to both sides to get

x2 + y2 − 10x − 14y − 7 + 25 = 25

same logic with the y terms

then factor the two perfect squares and move the other terms to the other side of the equation

you should end up w/ something like

(x-h)^2 + (y-k)^2 = r^2

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

be careful with signs