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

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