Answer:
center: (2,-4)
radius: 4
Step-by-step explanation:
Given Equation
x^2 - 4x + y^2 + 8y = - 4 Put brackets around the 1st and 2nd terms and another set of brackets around the 3rd and 4th terms
Solution
(x^2 - 4x) + (y^2 + 8y) = - 4 Add 4 to both sides
(x^2 - 4x) + (y^2 + 8y) +4 = - 4 +4 Combine the right
(x^2 - 4x) + (y^2 + 8y) +4 = -0 Take 1/2 of - 4x and square it
(x^2 - 4x + (-4/2)^2) + (y^2 + 8y) +4 = -0 Do the same to y
(x^2 - 4x + (-4/2)^2) + (y^2 + 8y +(8/2)^2) +4=0 Expand the squares.
(x^2 - 4x + 4) + (y^2 + 8y + 16)+4 =0
You have added a total of 4 + 16 to the inside of both sets of brackets. You have to subtract this amount from the 4 outside the brackets. By the way, you will always get 2 positive numbers that must be subtracted outside the brackets.
(x^2 - 4x + 4) + (y^2 + 8y + 16)+4 -20 =0 Write the squares of x and y
(x - 2)^2 + (y + 4)^2 - 16 = 0 Add 16 to both sides
(x - 2)^2 + (y + 4)^2 - 16 + 16 = 16 Combine
(x - 2)^2 + (y + 4)^2 = 16
The radius is found by taking the square root of 16
Radius = √16 = 4
The center is found by taking the integer inside the brackets and multiplying each of them by minus 1.
Center = -1(-2,4) = (2,-4)
