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mathdad
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= 1/3, not 1/4.RTCNTC said:3x^2 + 3y^2 + 5x - 4y = 1
3x^2 + 5x + 3y^2 - 4y = 1
x^2 + (5/3)x + y^2 -(4/3)y = 1/4
Again, the right side should be 1/3+ 25/36+ 4/9. 1/3, not 1/4.Half of (5/3) is (5/6). Then (5/6)^2 = (25/36).
Half of -(4/3) is -(2/3). Then (-2/3)^2 = (4/9).
We add (25/36) and (4/9) on both sides of the equation.
x^2 + (5/3)x + (25/36) + y^2 -(4/3)y + (4/9) = (1/4) + (25/36) + (4/9)
1/3+ 25/36+ 4/9= 12/36+ 25/36+ 16/36= 53/36Factor left side and calculate the right side.
(x + 5/6)(x + 5/6) + (y - 2/3)(y - 2/3) = (25/18)
(x + 5/6)^2 + (y - 2/3)^2 = (25/18)
Not the radius. The radius is sqrt(53}/6.The center is (h, k) = (-5/6, 2/3).
Let r = radius
r^2 = (25/18)
sqrt{r^2} = sqrt{25/18}
r = [5•sqrt{2}]/6
Is this correct?