Question

Complete the square to rewrite the following equation.identify the center and radius of the circle. You must show all work and calculation to receive credit.

X^2-4x+y^2+8y=-4

Answer 1

@angel

Answer 2

@hero

Answer 3

@dude

Answer 4

First group up similar terms for the sake of clarity
\(\left(x^{2}-4x\right)+\left(y^{2}+8y\right)=-4\)
Complete the square in each group. To find the \(y^2\) value, find \(b\) from \(2ab\) in each term. Then square it and set it as \(b^2\). Whatever you add should be added to the other side as well due to the addition property of equality.
\(\left(x^{2}-4x+4\right)+\left(y^{2}+8y+16\right)=-4+4+16\)
Simplify
\(\left(x-2\right)^{2}+\left(y+4\right)^{2}=16\)
Identify \((h,k)\) and \(r\). Center is (2, -4) and radius is 4

Answer 5

@AZ