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-4x2 + 9y2 + 16x - 18y +29 = 0 (I hope this is what you meant)

9y2 - 18y - (4x2 -16x) +29 = 0 (group together the x's and y's, and make the x2 term positive.

9(y2 - 2y) - 4(x2 - 4x) +29 = 0 (remove common factors)

9(y - 1)2 - 1 - 4(x - 2)2 - 4 + 29 = 0 (complete the squares)

9(y - 1)2 - 4(x - 2)2 = -25 (move constants to right-hand side)

[(y - 1)2] - 4[(x - 2)2]/9 = -25/9 (divide by coefficient in front of x or y bracket, in this case 9)

[(y - 1)2]/4 - [(x - 2)2]/9 = -25/36 (divide by coefficient in front of other bracket, in this case 4)

As you can see, we now have our equation in standard form. Our center points satisfy [(x - 2 = 0) , (y - 1 = 0)], thus our center is (2,1).

Q: What is the center of this hyperbola -4x2 plus 9y2 plus 16x-18y plus 29 equals 0?

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hyperbola

Center is (0, 0) . . . the origin.Radius is 7.

At the center, (x, y) = (-2, 5)

At the center, (x, y) = (-2, 5)

This not a circle, both the squared terms must have the same coefficients if it might be a circle. Different signs indicate a hyperbola.

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y2 - 5y + 2x - x2 - 120 is not a circle. It is a hyperbola rotated through 90 degrees.

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Center is (0, 0) . . . the origin.Radius is 7.

At the center, (x, y) = (-2, 5)

At the center, (x, y) = (-2, 5)

At the center, (x, y) = (-2, 5)

This not a circle, both the squared terms must have the same coefficients if it might be a circle. Different signs indicate a hyperbola.

(-4,-6)

(-7,5)

(-4,3)