anonymous
  • anonymous
The center of the circle that passes through the points (-2,3), (0,-3), and (4,-3) is________ a) (2,2) b) there is not enough data to find the center c) (1,2) d) (2,1)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
first we can find the eq of circle passing through three points, then can check the centre
anonymous
  • anonymous
how do I do that?
anonymous
  • anonymous
general eq of the circle is \[x^2+y^2+2gx+2fy+c=0\]

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anonymous
  • anonymous
substitute the three points in this eq we get three eqs in three unknows find the unknows g,f and c
anonymous
  • anonymous
centre is \[\sqrt{g^2+f^2-c}\]
anonymous
  • anonymous
for(-2,3) 4+9-4g+6f+c=0
anonymous
  • anonymous
for(0,-3) 9-6f+c=0
anonymous
  • anonymous
for(4,-3) 16+9+8g-6f+c=0
anonymous
  • anonymous
-4g+6f+c=-13 -6f+c=-9 8g-6f+c=-25
anonymous
  • anonymous
subtracting 1 n 3 -12g+12f=12 -g+f=1
anonymous
  • anonymous
sub 1 n 2 -4g+12f=-4 g-3f=1
anonymous
  • anonymous
adding the resultant eqs -2f=2 f=-1 which gives g=-2 n c=-3
anonymous
  • anonymous
center=(-g,-f)=(2,1)
anonymous
  • anonymous
so D is the right option:)
anonymous
  • anonymous
m sorry the formula i wrote earlier is to find the radius
anonymous
  • anonymous
thank you for your help
anonymous
  • anonymous
u got all the lenghy computations?
anonymous
  • anonymous
lengthy*
anonymous
  • anonymous
for the most part
anonymous
  • anonymous
what do g and f represent though?
anonymous
  • anonymous
if there is some confusion, u can ask:)
anonymous
  • anonymous
these r constants
anonymous
  • anonymous
the eq i wrote is the general eq of the circle
anonymous
  • anonymous
finding out g,f and c, we can find the eq of the circle
anonymous
  • anonymous
okay thank you
anonymous
  • anonymous
welcome:)

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