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 + 8y = −4
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
suppose i don't want to show all my work? can i get partial credit?
anonymous
  • anonymous
I don't want the answer. I want you to help me do it
anonymous
  • anonymous
the idea is to complete the square twice, once for \[x^2-4x\] and again for \[y^2+8y\]

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anonymous
  • anonymous
4x^2 and 8y^2
anonymous
  • anonymous
oh no
anonymous
  • anonymous
have you learned how to "complete the square"?
anonymous
  • anonymous
no
anonymous
  • anonymous
then you can't do this problem
anonymous
  • anonymous
oh
anonymous
  • anonymous
i will show you how to complete the square for \(x^2-4x\) what is half of 4?
anonymous
  • anonymous
2
anonymous
  • anonymous
right so we start with \[x^2-4x+y^2+8x=-4\]and turn it in to \[(x-2)^2+y^2+8y=-4+2^2\]
anonymous
  • anonymous
or\[(x-2)^2+y^2+8y=0\] now we repeat with \(y^2+8y\)
anonymous
  • anonymous
what is half of 8?
anonymous
  • anonymous
4
anonymous
  • anonymous
so we go right to \[(x-2)^2+(y+4)^2=0+4^2\]
anonymous
  • anonymous
or just \[(x-2)^2+(y+4)^2=16\] now your circle is in standard form and you can read off the center and radius from the equation
anonymous
  • anonymous
ok thank you
anonymous
  • anonymous
yw
anonymous
  • anonymous
I'm so sorry. when I look at numbers, they get mixed up in my head and I don't understand math in the first place.

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