What is 9x^2+4y^2+18x-27=0 ?

The solution to 9x^2+4y^2+18x-27=0 is Ellipse with (h,k)=(-1,0),a=2,b=3

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9x^2+4y^2+18x-27=0

9 x^{2} + 4 y^{2} + 18 x - 27 = 0

(h, k) = (- 1, 0), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 18 x - 27 = 0

Rewrite

9 x^{2} + 4 y^{2} + 18 x - 27 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 3, a = 2

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

\frac{x ^{2}}{20} + \frac{y ^{2}}{16} = 1

\frac{( x + 7 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1

49 x^{2} + y^{2} - 14 y = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 4

What is 9x^2+4y^2+18x-27=0 ?
The solution to 9x^2+4y^2+18x-27=0 is Ellipse with (h,k)=(-1,0),a=2,b=3