What is x^2+6x+9y^2-36y+36=0 ?

The solution to x^2+6x+9y^2-36y+36=0 is Ellipse with (h,k)=(-3,2),a=3,b=1

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x^2+6x+9y^2-36y+36=0

x^{2} + 6 x + 9 y^{2} - 36 y + 36 = 0

(h, k) = (- 3, 2), a = 3, b = 1

Solution steps

x^{2} + 6 x + 9 y^{2} - 36 y + 36 = 0

Rewrite

x^{2} + 6 x + 9 y^{2} - 36 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 2), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 2), a = 3, b = 1

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

x^{2} + 2 y^{2} = 2 x + 8

- 8 = 4 - 4 x^{2} - y^{2}

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

What is x^2+6x+9y^2-36y+36=0 ?
The solution to x^2+6x+9y^2-36y+36=0 is Ellipse with (h,k)=(-3,2),a=3,b=1