What is the axis 4x^2+25y^2+32x-250y+589=0 ?

The axis 4x^2+25y^2+32x-250y+589=0 is semi-major axis a=5, semi-minor axis b=2

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axis 4x^2+25y^2+32x-250y+589=0

axis

4 x^{2} + 25 y^{2} + 32 x - 250 y + 589 = 0

semi - major axis a = 5, semi - minor axis b = 2

Solution steps

4 x^{2} + 25 y^{2} + 32 x - 250 y + 589 = 0

Rewrite

4 x^{2} + 25 y^{2} + 32 x - 250 y + 589 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + y^{2} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{100} = 1

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

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

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

What is the axis 4x^2+25y^2+32x-250y+589=0 ?
The axis 4x^2+25y^2+32x-250y+589=0 is semi-major axis a=5, semi-minor axis b=2