What is the axis 9x^2+25y^2+18x+150y+9=0 ?

The axis 9x^2+25y^2+18x+150y+9=0 is semi-major axis a=5, semi-minor axis b=3

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axis 9x^2+25y^2+18x+150y+9=0

axis

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

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

Solution steps

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

Rewrite

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} + 144 y^{2} = 900

49 x^{2} + 16 y^{2} = 784

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1

What is the axis 9x^2+25y^2+18x+150y+9=0 ?
The axis 9x^2+25y^2+18x+150y+9=0 is semi-major axis a=5, semi-minor axis b=3