What is 36x^2+y^2-8y=0 ?

The solution to 36x^2+y^2-8y=0 is Ellipse with (h,k)=(0,4),a= 2/3 ,b=4

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36x^2+y^2-8y=0

36 x^{2} + y^{2} - 8 y = 0

(h, k) = (0, 4), a = \frac{2}{3}, b = 4

Solution steps

36 x^{2} + y^{2} - 8 y = 0

Rewrite

36 x^{2} + y^{2} - 8 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( y - 4 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 4), a = \frac{2}{3}, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 4), b = 4, a = \frac{2}{3}

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

0 = 16 - 4 x^{2} - y^{2}

4 x^{2} + 9 y^{2} + 8 x - 18 y - 23 = 0

x^{2} + 4 y^{2} - 4 x - 32 y + 32 = 0

\frac{( x - 1 ) ^{2}}{5} + \frac{( y + 2 ) ^{2}}{8} = 1

What is 36x^2+y^2-8y=0 ?
The solution to 36x^2+y^2-8y=0 is Ellipse with (h,k)=(0,4),a= 2/3 ,b=4