What is the center 10x^2-6y^2-20x-24y+46=0 ?

The center 10x^2-6y^2-20x-24y+46=0 is (1,-2)

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center 10x^2-6y^2-20x-24y+46=0

center

10 x^{2} - 6 y^{2} - 20 x - 24 y + 46 = 0

(1, - 2)

Solution steps

10 x^{2} - 6 y^{2} - 20 x - 24 y + 46 = 0

Rewrite

10 x^{2} - 6 y^{2} - 20 x - 24 y + 46 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( 10 ) ^{2}} - \frac{( x - 1 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = 10, b = 6

And the center is:

(1, - 2)

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

9 x^{2} - 16 y^{2} - 36 x + 96 y + 252 = 0

5 y^{2} - 16 x^{2} + 400 = 0

What is the center 10x^2-6y^2-20x-24y+46=0 ?
The center 10x^2-6y^2-20x-24y+46=0 is (1,-2)