What is 2x^2+2y^2-8y=0 ?

The solution to 2x^2+2y^2-8y=0 is Ellipse with (h,k)=(0,2),a=2,b=2

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2x^2+2y^2-8y=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

16 x^{2} + 16 y^{2} = 1 + 2 x + x^{2}

(\frac{x ^{2}}{9}) + (\frac{y ^{2}}{5}) = 1

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

What is 2x^2+2y^2-8y=0 ?
The solution to 2x^2+2y^2-8y=0 is Ellipse with (h,k)=(0,2),a=2,b=2