What is 9x^{(2)}+4y^{(2)}+36x-24y+36=0 ?

The solution to 9x^{(2)}+4y^{(2)}+36x-24y+36=0 is Ellipse with (h,k)=(-2,3),a=2,b=3

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 (y^{2} + 6 y + 9) + 16 (x^{2} - 4 x + 4) = 81 + 64

\frac{( x - h ) ^{2}}{b ^{2}} + \frac{( y - k ) ^{2}}{a ^{2}} = 1

25 x^{(2)} + 9 y^{(2)} + 50 x - 108 y + 124 = 0

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

\frac{x ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

What is 9x^{(2)}+4y^{(2)}+36x-24y+36=0 ?
The solution to 9x^{(2)}+4y^{(2)}+36x-24y+36=0 is Ellipse with (h,k)=(-2,3),a=2,b=3