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

\frac{x ^{2}}{8 0 ^{2}} + \frac{y ^{2}}{62. 5 ^{2}} = 1

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

9 y^{2} + 16 x^{2} = 144

\frac{( x - 2 ) ^{2}}{26} + \frac{( y - 3 ) ^{2}}{81} = 1

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

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