What is 2x^2+2y^2+20y=0 ?

The solution to 2x^2+2y^2+20y=0 is Ellipse with (h,k)=(0,-5),a=5,b=5

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2x^2+2y^2+20y=0

2 x^{2} + 2 y^{2} + 20 y = 0

(h, k) = (0, - 5), a = 5, b = 5

Solution steps

2 x^{2} + 2 y^{2} + 20 y = 0

Rewrite

2 x^{2} + 2 y^{2} + 20 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 5), a = 5, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 5), b = 5, a = 5

4 x^{2} + y^{2} - 6 y = 27

8 x^{2} + 16 x + 2 y^{2} = 0

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

\frac{( x - 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{64} = 1

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

What is 2x^2+2y^2+20y=0 ?
The solution to 2x^2+2y^2+20y=0 is Ellipse with (h,k)=(0,-5),a=5,b=5