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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} - 100 x + 36 y^{2} - 72 y = - 36

x^{2} + y^{2} \leq y

x^{2} + \frac{y ^{2}}{100} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{15} = 1

\frac{x ^{2}}{3} + \frac{y ^{2}}{9} = 1

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