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

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

x = 1 - y^{2}

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

y = \frac{1}{4} x^{2}

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

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