What is the center 2x^2-12x+y^2+6y+26=0 ?

The center 2x^2-12x+y^2+6y+26=0 is (3,-3)

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center 2x^2-12x+y^2+6y+26=0

center

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

(3, - 3)

Solution steps

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

Rewrite

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 3), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 3), b = 1, a = \frac{1}{2}

And the center is:

(3, - 3)

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

3 x^{2} + 4 y^{2} + 12 x - 8 y + 9 = 0

\frac{( x + 1 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{36} = 1

x^{2} + y^{2} \leq y

25 (x - 5)^{2} + 16 (y + 4)^{2} = 400

What is the center 2x^2-12x+y^2+6y+26=0 ?
The center 2x^2-12x+y^2+6y+26=0 is (3,-3)