What is (x^2)/(12)+(y^2)/(80)=1 ?

The solution to (x^2)/(12)+(y^2)/(80)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=4sqrt(5)

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(x^2)/(12)+(y^2)/(80)=1

\frac{x ^{2}}{12} + \frac{y ^{2}}{80} = 1

(h, k) = (0, 0), a = 23, b = 45

Solution steps

\frac{x ^{2}}{12} + \frac{y ^{2}}{80} = 1

Rewrite

\frac{x ^{2}}{12} + \frac{y ^{2}}{80} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 4 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23, b = 45

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 45, a = 23

4 x^{2} + 25 y^{2} = 1

x^{2} - 6 x + 4 y^{2} + 8 y - 3 = 0

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{25} = 1

2 x^{2} - 12 x + y^{2} + 6 y + 26 = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{49} = 1

What is (x^2)/(12)+(y^2)/(80)=1 ?
The solution to (x^2)/(12)+(y^2)/(80)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=4sqrt(5)