What is 60x^2+108y^2=6480 ?

The solution to 60x^2+108y^2=6480 is Ellipse with (h,k)=(0,0),a=6sqrt(3),b=2sqrt(15)

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60x^2+108y^2=6480

60 x^{2} + 108 y^{2} = 6480

(h, k) = (0, 0), a = 63, b = 215

Solution steps

60 x^{2} + 108 y^{2} = 6480

Rewrite

60 x^{2} + 108 y^{2} = 6480

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 15 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 63, b = 215

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 63, b = 215

22 x^{2} + 66 y^{2} + 60 x + 4 y + 9 = 0

2 x^{2} + 2 y^{2} + 36 y = 0

64 x^{2} + 81 y^{2} - 1152 x - 486 y + 729 = 0

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

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

What is 60x^2+108y^2=6480 ?
The solution to 60x^2+108y^2=6480 is Ellipse with (h,k)=(0,0),a=6sqrt(3),b=2sqrt(15)