What is 9x^2+4y^2-36x+24y-1=0 ?

The solution to 9x^2+4y^2-36x+24y-1=0 is Ellipse with (h,k)=(2,-3),a=(sqrt(73))/3 ,b=(sqrt(73))/2

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9x^2+4y^2-36x+24y-1=0

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

(h, k) = (2, - 3), a = \frac{73}{3}, b = \frac{73}{2}

Solution steps

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

Rewrite

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{73}{3} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{73}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{73}{3}, b = \frac{73}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = \frac{73}{2}, a = \frac{73}{3}

x^{2} + 2 y^{2} = 1

y^{2} + 2 x^{2} - 2 y + 4 x - 6 = 0

x^{2} + 3 y^{2} - 6 x + 6 y = 0

2 x^{2} + y^{2} = 50

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

What is 9x^2+4y^2-36x+24y-1=0 ?
The solution to 9x^2+4y^2-36x+24y-1=0 is Ellipse with (h,k)=(2,-3),a=(sqrt(73))/3 ,b=(sqrt(73))/2