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

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

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

y = x^{2} + 2 y^{2} - 6

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

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