What is 9x^2+36x+4y^2-24y+36=0 ?

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

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

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

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

Solution steps

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

Rewrite

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

\frac{( x - 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{25} = 1

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

\frac{( x - 4 ) ^{2}}{4.5} + \frac{( y - 1 ) ^{2}}{1} = 1

y = \frac{2 x - 4}{- 2 y + 4} x + 6

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

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