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

The solution to 2x^2-12x+y^2+6y+26=0 is Ellipse with (h,k)=(3,-3),a=sqrt(1/2),b=1

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

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

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

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}

\frac{x ^{2}}{9} + \frac{y ^{2}}{49} = 1

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

4 x^{2} + 9 y^{2} = 25

9 x^{2} + 49 y^{2} = 441

\frac{x ^{2}}{81} + \frac{y ^{2}}{16} = 1

What is 2x^2-12x+y^2+6y+26=0 ?
The solution to 2x^2-12x+y^2+6y+26=0 is Ellipse with (h,k)=(3,-3),a=sqrt(1/2),b=1