anonymous
  • anonymous
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
Mathematics
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@ganeshie8
freckles
  • freckles
ok first of all let's look at completing square: \[u^2+ku+(\frac{k}{2})^2=(u+\frac{k}{2})^2 \\ \text{ and you have } \\ x^2+4x+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \text{ what do you think we need \to replace } k \text{ with }?\]
freckles
  • freckles
notice comparing the thing that is in terms of x to the thing that is in terms of u we see that k is?

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freckles
  • freckles
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 ?

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