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}}{8} + \frac{y ^{2}}{5} = 1

x^{2} + 20 y^{2} - 2 x - 5 y = 0

9 x^{2} + 4 y^{2} - 36 x + 40 y + 100 = 0

x^{2} - 8 x + 25 y^{2} - 100 y + 91 = 0

25 x^{2} + y^{2} - 100 x - 2 y + 76 = 0

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