What is the axis x^2+4y^2=46 ?

The axis x^2+4y^2=46 is semi-major axis a=sqrt(46), semi-minor axis b=sqrt(23/2)

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axis x^2+4y^2=46

axis

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

semi - major axis a = 46, semi - minor axis b = \frac{23}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 46 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{23}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 46, b = \frac{23}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 46, b = \frac{23}{2}

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

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

x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{11} = 1

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

What is the axis x^2+4y^2=46 ?
The axis x^2+4y^2=46 is semi-major axis a=sqrt(46), semi-minor axis b=sqrt(23/2)