What is 9x^2+4y^2+18x-16y-11=0 ?

The solution to 9x^2+4y^2+18x-16y-11=0 is Ellipse with (h,k)=(-1,2),a=2,b=3

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( x + 5 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

0.25 x^{2} + y^{2} = 1

What is 9x^2+4y^2+18x-16y-11=0 ?
The solution to 9x^2+4y^2+18x-16y-11=0 is Ellipse with (h,k)=(-1,2),a=2,b=3