Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 + 4x + y2 − 6y = −4

Answer 1

@ganeshie8

Answer 2

ok first of all let's look at completing square:
\[u^2+ku+(\frac{k}{2})^2=(u+\frac{k}{2})^2 \\ \text{ and you have } \\ x^2+4x+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \text{ what do you think we need \to replace } k \text{ with }?\]

Answer 3

notice comparing the thing that is in terms of x to the thing that is in terms of u
we see that k is?

Answer 4

we see 4 is in place of the k
so k is 4
\[x^2+4x+(\frac{4}{2})^2=(x+\frac{4}{2})^2 \]
so let's go back to your equation:
\[x^2+4x+y^2-6y=-4 \\ \text{ add to both sides } (\frac{4}{2})^2 \\ x^2+4x+(\frac{4}{2})^2+y^2-6y=-4+(\frac{4}{2})^2 \\
(x+\frac{4}{2})^2+y^2-6y=-4+(\frac{4}{2})^2 \]
see if you can do the completing the square thing for the y part
\[u^2+ku+(\frac{k}{2})^2=(u+\frac{k}{2})^2 \\ y^2-6y+(\frac{k}{2})^2+(u+\frac{k}{2})^2 \]
what is k here ?