What is 9x^2+5y^2+18x+10y-31=0 ?

The solution to 9x^2+5y^2+18x+10y-31=0 is Ellipse with (h,k)=(-1,-1),a=sqrt(5),b=3

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9x^2+5y^2+18x+10y-31=0

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

(h, k) = (- 1, - 1), a = 5, b = 3

Solution steps

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

Rewrite

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 1), a = 5, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 1), b = 3, a = 5

x^{2} + 5 y^{2} + 10 y + 4 x - 27 = 0

x^{2} + 4 y^{2} \geq 100

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

9 x^{2} + 6 y^{2} + 36 y = 0

\frac{x ^{2}}{a} + \frac{y ^{2}}{b} = 1

What is 9x^2+5y^2+18x+10y-31=0 ?
The solution to 9x^2+5y^2+18x+10y-31=0 is Ellipse with (h,k)=(-1,-1),a=sqrt(5),b=3