What is the axis 25x^2-200x+y^2+4y+379=0 ?

The axis 25x^2-200x+y^2+4y+379=0 is semi-major axis b=5, semi-minor axis a=1

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axis 25x^2-200x+y^2+4y+379=0

axis

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

semi - major axis b = 5, semi - minor axis a = 1

Solution steps

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

Rewrite

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 1, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 5, a = 1

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 9 ) ^{2}}{25} = 1

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

25 x^{2} + 4 y^{2} = 100

What is the axis 25x^2-200x+y^2+4y+379=0 ?
The axis 25x^2-200x+y^2+4y+379=0 is semi-major axis b=5, semi-minor axis a=1