What is 2x^2+y^2-4=0 ?

The solution to 2x^2+y^2-4=0 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2

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2x^2+y^2-4=0

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

(h, k) = (0, 0), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = 2

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

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

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

What is 2x^2+y^2-4=0 ?
The solution to 2x^2+y^2-4=0 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2