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

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