What is 9x^2+y^2-18x-2y+1=0 ?

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

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9x^2+y^2-18x-2y+1=0

9 x^{2} + y^{2} - 18 x - 2 y + 1 = 0

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

Solution steps

9 x^{2} + y^{2} - 18 x - 2 y + 1 = 0

Rewrite

9 x^{2} + y^{2} - 18 x - 2 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

5 x^{2} + 9 y^{2} + 30 x - 36 y + 36 = 0

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

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

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

3 x^{2} + 3 y^{2} - 36 y = 0

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