Question

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

x2 + y2 + 16x − 14y − 150 = 0

center: (−8, 7)
center: (8, 7)
center: (7, 8)
center: (−7, 8)

Answer 1

Group your x stuff together and your y stuff together and move the constant over to the other side to start.
`( x^(2) +16x)+( y^(2)-14y)=150`. Now complete the squares on the x and y terms by taking half the linear terms (the x and y terms), squaring it, and then adding it to both sides. In the set of parenthesis with the x, the linear term is 16. Half of 16 is 8 and 8 squared is 64, so add it to both sides. Now for the y terms. In the set of parenthesis with the y, the linear term is 14. Half of 14 is 7 and 7 squared is 49. So add that in too. Now what you have is this:
`( x^(2) +16x+64)+( y^(2) -14y+49)=150+64+49` Simplifying that down into its perfect square binomials you have the equation for the circle now:
`(x+8) ^(2) +(y-7) ^(2)= 263`. The center then is (-8, 7)