anonymous
  • anonymous
I don't want anyone to give me the answer, I just need help understanding how to do it please!!
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
The general form of the equation of a circle is Ax2 + By2 + Cx + Dy + E = 0, where A = B 0. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle? a)A = 0, B = 0, C = 2, D = 2, and E = 3 b)A = 1, B = 1, C = 8, D = 0, and E = 9 c)A = 1, B = 1, C = 0, D = -8, and E = 7 d)A = 1, B = 1, C = -8, D = 0, and E = 0 e)A = 1, B = 1, C = 8, D = 8, and E = 3
welshfella
  • welshfella
if we write the equation of a circle as x^2 + y^2 + 2gx + 2fy + c = 0 then the center is (-g,-f) and the radius is sqrt(g^2 + f^2 - c) note there are no numbers before the x^2 and y^2 in the equation of a circle.
welshfella
  • welshfella
so for your circle you can see that A = 1 and B = 1

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anonymous
  • anonymous
sorry im horrible at math. so do you substitute A and B for X and Y? and D and E for G and F?
welshfella
  • welshfella
if we write the 2 equations together we can compare x^2 + y^2 + 2gx + 2fy + c = 0 Ax^2+ By^2 + Cx + Dy + e = 0 can you see that A and B = 1?
welshfella
  • welshfella
note x^2 is same as 1x^2
anonymous
  • anonymous
ok, so would the answer be B?
welshfella
  • welshfella
we dont know that yet we need to find C D and E the center is at (0,4) meaning x = 0 and y = 4 if we compare this with (-g,-f) we see that -g = 0 so C =0 Follow?
welshfella
  • welshfella
and in the case of y = 4 , -f = 4 so f = -4 and 2f = -8 making D = 2f = -8
anonymous
  • anonymous
ok
welshfella
  • welshfella
now to work out e(which = c) we need to solve radius r = sqrt(g^2 + f^2 - c) 3 = sqrt(0^2 + (-4)2 - e)
welshfella
  • welshfella
9 = 16 - e
welshfella
  • welshfella
so find e and you have your result
anonymous
  • anonymous
oh so its C. thank you for showing me how to do it
welshfella
  • welshfella
yw
welshfella
  • welshfella
yes e = 7 so its C
welshfella
  • welshfella
by writing the 2 equations together we can see that C - 2g , D = 2f and E = c
welshfella
  • welshfella
- that's called comparing coefficients
anonymous
  • anonymous
thank you =D

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