What is 9x^2+y^2+18x+4y+4=0 ?

The solution to 9x^2+y^2+18x+4y+4=0 is Ellipse with (h,k)=(-1,-2),a=1,b=3

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9x^2+y^2+18x+4y+4=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + y^{2} - 16 x - 6 y + 21 = 0

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

18 x^{2} + 24 x + 12 y^{2} - 12 y = 1

16 x^{2} + 25 y^{2} - 64 x - 50 y - 311 = 0

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

What is 9x^2+y^2+18x+4y+4=0 ?
The solution to 9x^2+y^2+18x+4y+4=0 is Ellipse with (h,k)=(-1,-2),a=1,b=3