anonymous
  • anonymous
The equation of a circle is in the form x^2 +y^2 +Cx+Dy+E=. Find an equation of the circle shown in the illustration by determining C,D, and E
Mathematics
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anonymous
  • anonymous
The equation of a circle is in the form x^2 +y^2 +Cx+Dy+E=. Find an equation of the circle shown in the illustration by determining C,D, and E
Mathematics
jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
where is the illustration, please?
anonymous
  • anonymous
|dw:1444143802955:dw|
Michele_Laino
  • Michele_Laino
here as we can see the center of your circumference is at point \((3,0)\)

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Michele_Laino
  • Michele_Laino
sorry, we have to replace the coordinates of the points you provided, into your generic equation
anonymous
  • anonymous
How? I'm so confused
Michele_Laino
  • Michele_Laino
for examnple, your circumference passes at point \((0,0)\) so I replace \(x=0,y=0\) into your equation, so I get this: \[{0^2} + {0^2} + C \cdot 0 + D \cdot 0 + E = 0\] what is \(E\)?
anonymous
  • anonymous
Even plug in the points (3,3) and (6,0)?
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
okay thank you so much
Michele_Laino
  • Michele_Laino
:)
anonymous
  • anonymous
anonymous
  • anonymous
I have to write and solve a system of three equations in the three unknowns C, D, and E. Then write the equation of the circle in general form:
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
yes! correct! As you can see we have an algebraic system with 2 unknowns, since we have already determined E as \(E=0\)
anonymous
  • anonymous
But don't we have to come up with 3 systems
Michele_Laino
  • Michele_Laino
if we replace \(x=3,y=3\) into your equation,we get: 9+9+3C+3D=0 that is the first equation of our system, the first one is E=0
Michele_Laino
  • Michele_Laino
if we replace \(x=6,y=0\), we get: 36+0+6C+0.D=0 that is the third equation
Michele_Laino
  • Michele_Laino
please solve those new equations with respect to C and D

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