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

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

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

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

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

Solution steps

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

Rewrite

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 9 y^{2} - 8 x + 36 y - 104 = 0

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

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

25 y^{2} + 16 x^{2} + 50 y - 64 x - 311 = 0

25 x^{2} + 100 y^{2} = 400

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