What is 9x^2+y^2-18x-6y+9=0 ?

The solution to 9x^2+y^2-18x-6y+9=0 is Ellipse with (h,k)=(1,3),a=1,b=3

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9x^2+y^2-18x-6y+9=0

9 x^{2} + y^{2} - 18 x - 6 y + 9 = 0

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

Solution steps

9 x^{2} + y^{2} - 18 x - 6 y + 9 = 0

Rewrite

9 x^{2} + y^{2} - 18 x - 6 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 x^{2} + 10 y^{2} = 50

\frac{( x + 5 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{64} = 1

2 x^{2} + 7 y^{2} = 14

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

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

What is 9x^2+y^2-18x-6y+9=0 ?
The solution to 9x^2+y^2-18x-6y+9=0 is Ellipse with (h,k)=(1,3),a=1,b=3