What is 2x^2+2y^2-40y=0 ?

The solution to 2x^2+2y^2-40y=0 is Ellipse with (h,k)=(0,10),a=10,b=10

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2x^2+2y^2-40y=0

2 x^{2} + 2 y^{2} - 40 y = 0

(h, k) = (0, 10), a = 10, b = 10

Solution steps

2 x^{2} + 2 y^{2} - 40 y = 0

Rewrite

2 x^{2} + 2 y^{2} - 40 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 0 ^{2}} + \frac{( y - 10 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 10), a = 10, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 10), b = 10, a = 10

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} \geq 0

\frac{2 y}{1 - x ^{2} - y ^{2}} = \frac{1}{2}

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

4 x^{2} + y^{2} - 16 x + 6 y - 75 = 0

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

What is 2x^2+2y^2-40y=0 ?
The solution to 2x^2+2y^2-40y=0 is Ellipse with (h,k)=(0,10),a=10,b=10