What is the axis 3x^2+y^2-24x+39=0 ?

The axis 3x^2+y^2-24x+39=0 is semi-major axis b=3, semi-minor axis a=sqrt(3)

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axis 3x^2+y^2-24x+39=0

axis

3 x^{2} + y^{2} - 24 x + 39 = 0

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

Solution steps

3 x^{2} + y^{2} - 24 x + 39 = 0

Rewrite

3 x^{2} + y^{2} - 24 x + 39 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 0), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 0), b = 3, a = 3

\frac{x ^{2}}{5} + \frac{y ^{2}}{9} = 1

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

x^{2} + 4 y^{2} = 46

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

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

What is the axis 3x^2+y^2-24x+39=0 ?
The axis 3x^2+y^2-24x+39=0 is semi-major axis b=3, semi-minor axis a=sqrt(3)