What is 12x^2+5y^2-60=0 ?

The solution to 12x^2+5y^2-60=0 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=2sqrt(3)

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12x^2+5y^2-60=0

12 x^{2} + 5 y^{2} - 60 = 0

(h, k) = (0, 0), a = 5, b = 23

Solution steps

12 x^{2} + 5 y^{2} - 60 = 0

Rewrite

12 x^{2} + 5 y^{2} - 60 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 23, a = 5

9 x^{2} + 16 y^{2} + 96 y - 36 x + 36 = 0

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

4 x^{2} + 16 y^{2} - 64 = 1

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

\frac{( x - 6 ) ^{2}}{36} + \frac{y ^{2}}{100} = 1

What is 12x^2+5y^2-60=0 ?
The solution to 12x^2+5y^2-60=0 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=2sqrt(3)