What is the axis 36x^2+11y^2+144x+44y-208=0 ?

The axis 36x^2+11y^2+144x+44y-208=0 is semi-major axis b=6, semi-minor axis a=sqrt(11)

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axis 36x^2+11y^2+144x+44y-208=0

axis

36 x^{2} + 11 y^{2} + 144 x + 44 y - 208 = 0

semi - major axis b = 6, semi - minor axis a = 11

Solution steps

36 x^{2} + 11 y^{2} + 144 x + 44 y - 208 = 0

Rewrite

36 x^{2} + 11 y^{2} + 144 x + 44 y - 208 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( 11 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 2), a = 11, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 2), b = 6, a = 11

9 x^{2} + 16 y^{2} + 90 x + 32 y + 97 = 0

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

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

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

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

What is the axis 36x^2+11y^2+144x+44y-208=0 ?
The axis 36x^2+11y^2+144x+44y-208=0 is semi-major axis b=6, semi-minor axis a=sqrt(11)