What is 9x^2+36y^2+36x-216y+36=0 ?

The solution to 9x^2+36y^2+36x-216y+36=0 is Ellipse with (h,k)=(-2,3),a=6,b=3

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9x^2+36y^2+36x-216y+36=0

9 x^{2} + 36 y^{2} + 36 x - 216 y + 36 = 0

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

Solution steps

9 x^{2} + 36 y^{2} + 36 x - 216 y + 36 = 0

Rewrite

9 x^{2} + 36 y^{2} + 36 x - 216 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{1} = 1

25 x^{2} + 16 y^{2} - 400 = 0

4 x^{2} + 9 y^{2} - 24 x - 36 y + 36 = 0

x^{2} + 9 y^{2} = 3

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 6 ) ^{2}}{\frac{3}{2}} = 1

What is 9x^2+36y^2+36x-216y+36=0 ?
The solution to 9x^2+36y^2+36x-216y+36=0 is Ellipse with (h,k)=(-2,3),a=6,b=3