What is 9x^2+y^2-54x-6y+81=0 ?

The solution to 9x^2+y^2-54x-6y+81=0 is Ellipse with (h,k)=(3,3),a=1,b=3

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9x^2+y^2-54x-6y+81=0

9 x^{2} + y^{2} - 54 x - 6 y + 81 = 0

(h, k) = (3, 3), a = 1, b = 3

Solution steps

9 x^{2} + y^{2} - 54 x - 6 y + 81 = 0

Rewrite

9 x^{2} + y^{2} - 54 x - 6 y + 81 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 3), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 3), b = 3, a = 1

x^{2} = \frac{4 - y ^{2}}{2}

64 x^{2} - 192 x - 156 + 100 y^{2} - 200 y = 0

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{81} = 1

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

What is 9x^2+y^2-54x-6y+81=0 ?
The solution to 9x^2+y^2-54x-6y+81=0 is Ellipse with (h,k)=(3,3),a=1,b=3