anonymous
  • anonymous
how do i get the center, vertices, foci, and eccentricity of 9x^2+4y^2-36x+8y_31=0?
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
it looks like the equation for a circle or ellipse
amistre64
  • amistre64
(9x^2 -36x +n) + (4y^2 +8y +m) = 31 +n+m complete the squares to find n and m
amistre64
  • amistre64
n = (36/2)^2 m=(8/2)^2 (9x^2 -36x +18^2) + (4y^2 +8y + 4^2) = 31+18^2+4^2

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amistre64
  • amistre64
9(x^2 -4x + 9^3) + 4(y^2 +2y + 4) = 371.... if i did it right in me head
amistre64
  • amistre64
(3x - 18)^2 + (2y +4)^2 = 371 3(x-6)^2 + 2(y+2)^2 = 371 is what I ge so far
amistre64
  • amistre64
divide evertyhing by 371 and see what you can work out I guess...
amistre64
  • amistre64
and dont do stupid mistakes like I did..... that 3 and 2 dont get pulled out....
amistre64
  • amistre64
9(x^2 -4x + 9^3) + 4(y^2 +2y + 4) = 371 is the correct way... solve your quadratics to get 2 solutions.....
amistre64
  • amistre64
im gonna get it one way or another..... ignore that 9^3 flub... 9(x^2 -4x + 36) + 4(y^2 +2y + 4) = 371

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