What is 9x^2+4y^2-18x+24y=0 ?

The solution to 9x^2+4y^2-18x+24y=0 is Ellipse with (h,k)=(1,-3),a=sqrt(5),b=(3sqrt(5))/2

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9x^2+4y^2-18x+24y=0

9 x^{2} + 4 y^{2} - 18 x + 24 y = 0

(h, k) = (1, - 3), a = 5, b = \frac{3 5}{2}

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 24 y = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 24 y = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{3 5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 5, b = \frac{3 5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = \frac{3 5}{2}, a = 5

27 x^{2} + 48 y^{2} = 192 y + 54 x + 213

x, x^{2} + \frac{π R ( x ) ^{2}}{2} = 200

\frac{( x ^{2} )}{( 29 )} + \frac{( y ^{2} )}{( 24 )} = 1

36 x^{2} + 16 y^{2} + 96 y - 180 x - 207 = 0

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

What is 9x^2+4y^2-18x+24y=0 ?
The solution to 9x^2+4y^2-18x+24y=0 is Ellipse with (h,k)=(1,-3),a=sqrt(5),b=(3sqrt(5))/2