anonymous
  • anonymous
Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x^2 − 4x + y^2 + 8y = −4
Mathematics
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SOLVED
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katieb
  • katieb
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AlexandervonHumboldt2
  • AlexandervonHumboldt2
first you need to convert this equation to (x-h)^2+(y-k)^2=r^2 where r is radius
anonymous
  • anonymous
I know that 4 is the radius but I just cant find the rest of it.
AlexandervonHumboldt2
  • AlexandervonHumboldt2
x^2 − 4x + y^2 + 8y = −4 (x^2-4x) + (y^2-6y)=-4 (x^2-4x+4)+(y^2-6y+9)=-4+4+9 (x-2)^2+(y-3)^2=9

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AlexandervonHumboldt2
  • AlexandervonHumboldt2
thus the radius is sqrt9=3, and the center is (2, 3)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
(x-h)^2+(y-k)^2=r^2 where r is radius and (h, k) is center
anonymous
  • anonymous
Oh.. Thank you for explaining it to me and working it out :).
AlexandervonHumboldt2
  • AlexandervonHumboldt2
wait i made amistake
AlexandervonHumboldt2
  • AlexandervonHumboldt2
wait
anonymous
  • anonymous
Oh. okay!
AlexandervonHumboldt2
  • AlexandervonHumboldt2
it should be: x^2 − 4x + y^2 + 8y = −4 (x^2-4x)+(y^2+8y)=-4 (x^2-4x+4)+(y^2+8y+16)=-4+16+4 (x-2)^2+(y+4)^2=16 thus the center is (2, -4) and radius is sqrt16=4
anonymous
  • anonymous
Thank you! :)

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