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

The axis 25x^2+9y^2-100x+18y-116=0 is semi-major axis b=5, semi-minor axis a=3

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

axis

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

semi - major axis b = 5, semi - minor axis a = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

3 x^{2} + y^{2} + 2 x - 6 y = 3

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

What is the axis 25x^2+9y^2-100x+18y-116=0 ?
The axis 25x^2+9y^2-100x+18y-116=0 is semi-major axis b=5, semi-minor axis a=3