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

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

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axis x^2+4y^2=25

axis

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

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

3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

\frac{( x - 4 ) ^{2}}{81} + \frac{( y + 9 ) ^{2}}{4} = 1

x^{2} + y^{2} + 10 x - 8 y = - 32

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