What is 9x^2+4y^2+18x-8y-131=0 ?

The solution to 9x^2+4y^2+18x-8y-131=0 is Ellipse with (h,k)=(-1,1),a=4,b=6

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9x^2+4y^2+18x-8y-131=0

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

(h, k) = (- 1, 1), a = 4, b = 6

Solution steps

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

Rewrite

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{4 ^{2}} + \frac{( y - 1 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 6, a = 4

2 x^{2} - 8 x + y^{2} + 6 y + 15 = 0

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

x^{2} + 4 y^{2} + 2 x - 12 y + 2 = 0

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

What is 9x^2+4y^2+18x-8y-131=0 ?
The solution to 9x^2+4y^2+18x-8y-131=0 is Ellipse with (h,k)=(-1,1),a=4,b=6