What is x^2-2x^2-2y^2-12=0 ?

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

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x^2-2x^2-2y^2-12=0

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

(h, k) = (0, 0), a = 23, b = 6

Solution steps

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

Rewrite

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 23, b = 6

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

\frac{( y - 2 ) ^{2}}{9} + \frac{( x - 3 ) ^{2}}{16} = 1

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{4} = 1

6 x^{2} + 96 x + 16 y^{2} - 40 y = 315

(\frac{x - 2}{16})^{2} + (\frac{y + 3}{9})^{2} = 1

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