What is the center 64x^2+100y^2+768x-600y-3196=0 ?

The center 64x^2+100y^2+768x-600y-3196=0 is (-6,3)

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center 64x^2+100y^2+768x-600y-3196=0

center

64 x^{2} + 100 y^{2} + 768 x - 600 y - 3196 = 0

(- 6, 3)

Solution steps

64 x^{2} + 100 y^{2} + 768 x - 600 y - 3196 = 0

Rewrite

64 x^{2} + 100 y^{2} + 768 x - 600 y - 3196 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 3 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 3), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 3), a = 10, b = 8

And the center is:

(- 6, 3)

2 x^{2} + 3 y^{2} - 4 x + 6 y - 1 = 0

x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

4 x^{2} + 25 y^{2} = 100

2 (x + \frac{1}{4})^{2} + y^{2} = 8

x^{2} + 4 y^{2} = 16

What is the center 64x^2+100y^2+768x-600y-3196=0 ?
The center 64x^2+100y^2+768x-600y-3196=0 is (-6,3)