What is the axis 25x^2+16y^2+100x+96y-156=0 ?

The axis 25x^2+16y^2+100x+96y-156=0 is semi-major axis b=5, semi-minor axis a=4

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axis 25x^2+16y^2+100x+96y-156=0

axis

25 x^{2} + 16 y^{2} + 100 x + 96 y - 156 = 0

semi - major axis b = 5, semi - minor axis a = 4

Solution steps

25 x^{2} + 16 y^{2} + 100 x + 96 y - 156 = 0

Rewrite

25 x^{2} + 16 y^{2} + 100 x + 96 y - 156 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 3), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 3), b = 5, a = 4

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

3 x^{2} + 7 y^{2} = 63

x^{2} + 4 y^{2} = 25

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

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

What is the axis 25x^2+16y^2+100x+96y-156=0 ?
The axis 25x^2+16y^2+100x+96y-156=0 is semi-major axis b=5, semi-minor axis a=4