What is 36x^2+9y^2+36y-288=0 ?

The solution to 36x^2+9y^2+36y-288=0 is Ellipse with (h,k)=(0,-2),a=3,b=6

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36x^2+9y^2+36y-288=0

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

(h, k) = (0, - 2), a = 3, b = 6

Solution steps

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

Rewrite

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 2), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), b = 6, a = 3

3 x^{2} + 4 y^{2} = 16

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

9 x^{2} + 25 y^{2} - 225 = 0

4 y^{2} - 16 y + x^{2} + 2 x = - 1

9 x^{2} + 25 y^{2} - 36 x + 150 y + 36 = 0

What is 36x^2+9y^2+36y-288=0 ?
The solution to 36x^2+9y^2+36y-288=0 is Ellipse with (h,k)=(0,-2),a=3,b=6