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

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

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x^2+2y^2+2x-2y=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x, x^{2} + 5 Y (x)^{2} + 2 x - 30 Y + 36 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{49} = 1

\frac{( x - 1 ) ^{2}}{8} + \frac{( y + \frac{3}{2} ) ^{2}}{4} = 1

11 x^{2} + 9 y^{2} = 1

x^{2} + y^{2} + 36 y = 0

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