What is 2x^2-3y^2-12x-24y+60=0 ?

The solution to 2x^2-3y^2-12x-24y+60=0 is Hyperbola with (h,k)=(3,-4),a=sqrt(30),b=3sqrt(5)

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2x^2-3y^2-12x-24y+60=0

2 x^{2} - 3 y^{2} - 12 x - 24 y + 60 = 0

(h, k) = (3, - 4), a = 30, b = 35

Solution steps

2 x^{2} - 3 y^{2} - 12 x - 24 y + 60 = 0

Rewrite

2 x^{2} - 3 y^{2} - 12 x - 24 y + 60 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 30 ) ^{2}} - \frac{( x - 3 ) ^{2}}{( 3 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, - 4), a = 30, b = 35

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

3 x^{2} - y^{2} - 12 = 0

\frac{y ^{2}}{25} - \frac{x ^{2}}{25} = 1

2 x^{(2)} - 2 y^{(2)} - 20 x + 16 y + 16 = 0

x^{2} - 6 x - y^{2} - 2 y = 9

What is 2x^2-3y^2-12x-24y+60=0 ?
The solution to 2x^2-3y^2-12x-24y+60=0 is Hyperbola with (h,k)=(3,-4),a=sqrt(30),b=3sqrt(5)