What is 9x^2+4y^2-18x+24y=36 ?

The solution to 9x^2+4y^2-18x+24y=36 is Ellipse with (h,k)=(1,-3),a=3,b= 9/2

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9x^2+4y^2-18x+24y=36

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

(h, k) = (1, - 3), a = 3, b = \frac{9}{2}

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{9}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 3, b = \frac{9}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = \frac{9}{2}, a = 3

9 > x^{2} + 9 y^{2}

27 x^{2} + 6 y^{2} - 5 = 0

- 1 = (\frac{( x - 0 )}{1 ^{2}})^{2} + (\frac{( y - 1 )}{1 ^{2}})^{2}

\frac{u + v}{u ^{2} + v ^{2}} + \frac{- v + u}{u ^{2} + v ^{2}} = 1

12 (x + 4)^{2} + 3 (y - 1)^{2} = 48

What is 9x^2+4y^2-18x+24y=36 ?
The solution to 9x^2+4y^2-18x+24y=36 is Ellipse with (h,k)=(1,-3),a=3,b= 9/2