What is 2x^2+2y^2+36y=0 ?

The solution to 2x^2+2y^2+36y=0 is Ellipse with (h,k)=(0,-9),a=9,b=9

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2x^2+2y^2+36y=0

2 x^{2} + 2 y^{2} + 36 y = 0

(h, k) = (0, - 9), a = 9, b = 9

Solution steps

2 x^{2} + 2 y^{2} + 36 y = 0

Rewrite

2 x^{2} + 2 y^{2} + 36 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{9 ^{2}} + \frac{( y - ( - 9 ) ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 9), a = 9, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 9), b = 9, a = 9

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

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

\frac{( y - 1 ) ^{2}}{2} + \frac{5 ( x + 2 ) ^{2}}{3} = 2

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

\frac{( x + 1 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{4} = 1

What is 2x^2+2y^2+36y=0 ?
The solution to 2x^2+2y^2+36y=0 is Ellipse with (h,k)=(0,-9),a=9,b=9