What is the axis 41x^2+16y^2+246x-192y+289=0 ?

The axis 41x^2+16y^2+246x-192y+289=0 is semi-major axis b=sqrt(41), semi-minor axis a=4

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axis 41x^2+16y^2+246x-192y+289=0

axis

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

semi - major axis b = 41, semi - minor axis a = 4

Solution steps

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

Rewrite

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{4 ^{2}} + \frac{( y - 6 ) ^{2}}{( 41 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 6), a = 4, b = 41

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 6), b = 41, a = 4

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

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

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

What is the axis 41x^2+16y^2+246x-192y+289=0 ?
The axis 41x^2+16y^2+246x-192y+289=0 is semi-major axis b=sqrt(41), semi-minor axis a=4