What is x^2+2y^2-4y=6 ?

The solution to x^2+2y^2-4y=6 is Ellipse with (h,k)=(0,1),a=2sqrt(2),b=2

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x^2+2y^2-4y=6

x^{2} + 2 y^{2} - 4 y = 6

(h, k) = (0, 1), a = 22, b = 2

Solution steps

x^{2} + 2 y^{2} - 4 y = 6

Rewrite

x^{2} + 2 y^{2} - 4 y = 6

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 1), a = 22, b = 2

2 x^{2} + 4 y^{2} = 1

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{9} = 1

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

x^{2} + 4 y^{2} + 10 x + 10 y - 8 = 0

What is x^2+2y^2-4y=6 ?
The solution to x^2+2y^2-4y=6 is Ellipse with (h,k)=(0,1),a=2sqrt(2),b=2