What is 9x^2-54x+y^2-2y=-81 ?

The solution to 9x^2-54x+y^2-2y=-81 is Ellipse with (h,k)=(3,1),a= 1/3 ,b=1

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9x^2-54x+y^2-2y=-81

9 x^{2} - 54 x + y^{2} - 2 y = - 81

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

Solution steps

9 x^{2} - 54 x + y^{2} - 2 y = - 81

Rewrite

9 x^{2} - 54 x + y^{2} - 2 y = - 81

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{81} = 1

3 x^{2} + y^{2} = 52

(\frac{x ^{2}}{25}) + (\frac{y ^{2}}{9}) = 1

8 x^{2} + 16 x + 4 y^{2} - 12 y = 15

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{9} = 1

What is 9x^2-54x+y^2-2y=-81 ?
The solution to 9x^2-54x+y^2-2y=-81 is Ellipse with (h,k)=(3,1),a= 1/3 ,b=1