What is 0=1+2x^2+2y^2 ?

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

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0=1+2x^2+2y^2

0 = 1 + 2 x^{2} + 2 y^{2}

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

0 = 1 + 2 x^{2} + 2 y^{2}

Rewrite

0 - 1 - 2 x^{2} - 2 y^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{2}, a = \frac{1}{2}

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

16 x^{2} + 9 y^{2} - 32 x + 54 y - 47 = 0

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

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

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

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