What is 9x^2+25y^2+18x+100y-116=0 ?

The solution to 9x^2+25y^2+18x+100y-116=0 is Ellipse with (h,k)=(-1,-2),a=5,b=3

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9x^2+25y^2+18x+100y-116=0

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

(h, k) = (- 1, - 2), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

Rewrite

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 2), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 2), a = 5, b = 3

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

x^{(2)} + 4 x + 4 y^{(2)} - 6 y + 9 = 3

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

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

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

What is 9x^2+25y^2+18x+100y-116=0 ?
The solution to 9x^2+25y^2+18x+100y-116=0 is Ellipse with (h,k)=(-1,-2),a=5,b=3