What is the axis ((x-30)^2)/(40^2)+(y^2)/(2^2)=1 ?

The axis ((x-30)^2)/(40^2)+(y^2)/(2^2)=1 is semi-major axis a=40, semi-minor axis b=2

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axis ((x-30)^2)/(40^2)+(y^2)/(2^2)=1

axis

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

semi - major axis a = 40, semi - minor axis b = 2

Solution steps

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

Rewrite

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (30, 0), a = 40, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (30, 0), a = 40, b = 2

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

4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

5 x^{2} + 2 y^{2} = 50

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{16} = 1

What is the axis ((x-30)^2)/(40^2)+(y^2)/(2^2)=1 ?
The axis ((x-30)^2)/(40^2)+(y^2)/(2^2)=1 is semi-major axis a=40, semi-minor axis b=2