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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{80} = 1

4 x^{2} + y^{2} - 16 x + 2 y + 1 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

2 x^{2} + y^{2} + 16 x - 4 y + 32 = 0

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