What is the axis 16x^2+4y^2=25 ?

The axis 16x^2+4y^2=25 is semi-major axis b= 5/2 , semi-minor axis a= 5/4

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axis 16x^2+4y^2=25

axis

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

semi - major axis b = \frac{5}{2}, semi - minor axis a = \frac{5}{4}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{4}, b = \frac{5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{5}{2}, a = \frac{5}{4}

4 x^{2} + 9 y^{2} - 36 = 0

5 x^{2} + 9 y^{2} - 10 x - 36 y = 4

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

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

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

What is the axis 16x^2+4y^2=25 ?
The axis 16x^2+4y^2=25 is semi-major axis b= 5/2 , semi-minor axis a= 5/4