What is 9x^2+18x+4y^2-24y+9=0 ?

The solution to 9x^2+18x+4y^2-24y+9=0 is Ellipse with (h,k)=(-1,3),a=2,b=3

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9x^2+18x+4y^2-24y+9=0

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

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

Solution steps

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

Rewrite

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

x^{2} + 3 y^{2} - 4 x + y = 12

2 x^{2} + 3 y^{2} = 4

\frac{( x - 1 ) ^{2}}{49} + \frac{( y - 3 ) ^{2}}{36} = 1

(2 x - 9)^{2} + (y)^{2} = 5^{2}

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

What is 9x^2+18x+4y^2-24y+9=0 ?
The solution to 9x^2+18x+4y^2-24y+9=0 is Ellipse with (h,k)=(-1,3),a=2,b=3