What is the axis 9x^2+25y^2-36x-50y+60=0 ?

The axis 9x^2+25y^2-36x-50y+60=0 is semi-major axis a= 1/3 , semi-minor axis b= 1/5

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axis 9x^2+25y^2-36x-50y+60=0

axis

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

semi - major axis a = \frac{1}{3}, semi - minor axis b = \frac{1}{5}

Solution steps

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = \frac{1}{3}, b = \frac{1}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = \frac{1}{3}, b = \frac{1}{5}

25 x^{2} + 4 y^{2} = 100

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

\frac{x ^{2}}{100} + \frac{y ^{2}}{36} = 1

9 x^{2} + 4 y^{2} - 18 x + 16 y - 11 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

What is the axis 9x^2+25y^2-36x-50y+60=0 ?
The axis 9x^2+25y^2-36x-50y+60=0 is semi-major axis a= 1/3 , semi-minor axis b= 1/5