What is 2x^2+2y^2-24y=0 ?

The solution to 2x^2+2y^2-24y=0 is Ellipse with (h,k)=(0,6),a=6,b=6

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2x^2+2y^2-24y=0

2 x^{2} + 2 y^{2} - 24 y = 0

(h, k) = (0, 6), a = 6, b = 6

Solution steps

2 x^{2} + 2 y^{2} - 24 y = 0

Rewrite

2 x^{2} + 2 y^{2} - 24 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 6), a = 6, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 6), b = 6, a = 6

y^{2} + 4 x^{2} = 128

2 x^{2} + 3 y^{2} + 10 x + 9 y - 19 = 0

2 (x - 3)^{2} + 3 (y - 2)^{2} = 6

(\frac{x ^{2}}{15}) + ((\frac{( y - 8 )}{49})^{2}) = 1

100 - 25 x^{2} - 4 y^{2} \geq 0

What is 2x^2+2y^2-24y=0 ?
The solution to 2x^2+2y^2-24y=0 is Ellipse with (h,k)=(0,6),a=6,b=6