What is the axis x^2+4y^2-6x-16y=36 ?

The axis x^2+4y^2-6x-16y=36 is semi-major axis a=sqrt(61), semi-minor axis b=(sqrt(61))/2

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axis x^2+4y^2-6x-16y=36

axis

x^{2} + 4 y^{2} - 6 x - 16 y = 36

semi - major axis a = 61, semi - minor axis b = \frac{61}{2}

Solution steps

x^{2} + 4 y^{2} - 6 x - 16 y = 36

Rewrite

x^{2} + 4 y^{2} - 6 x - 16 y = 36

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 61 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{61}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 2), a = 61, b = \frac{61}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 2), a = 61, b = \frac{61}{2}

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

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

16 x^{2} + 9 y^{2} - 144 = 0

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

\frac{x ^{2}}{56} + \frac{y ^{2}}{36} = 1

What is the axis x^2+4y^2-6x-16y=36 ?
The axis x^2+4y^2-6x-16y=36 is semi-major axis a=sqrt(61), semi-minor axis b=(sqrt(61))/2