What is 6x^2-5y^2+12x-30y-9=0 ?

The solution to 6x^2-5y^2+12x-30y-9=0 is Hyperbola with (h,k)=(-1,-3),a=sqrt(6),b=sqrt(5)

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6x^2-5y^2+12x-30y-9=0

6 x^{2} - 5 y^{2} + 12 x - 30 y - 9 = 0

(h, k) = (- 1, - 3), a = 6, b = 5

Solution steps

6 x^{2} - 5 y^{2} + 12 x - 30 y - 9 = 0

Rewrite

6 x^{2} - 5 y^{2} + 12 x - 30 y - 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( 6 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 3), a = 6, b = 5

18 y^{2} - 4 x^{2} = 1

1 1^{2} - x^{2} + y^{2} = 9^{2}

9 (x - 3)^{2} - 4 (y - 1)^{2} = - 36

x^{2} - y^{2} - 2 x - 2 y - 1 = 0

x, h (x)^{2} = 13 x^{2} - 6 x + 1

What is 6x^2-5y^2+12x-30y-9=0 ?
The solution to 6x^2-5y^2+12x-30y-9=0 is Hyperbola with (h,k)=(-1,-3),a=sqrt(6),b=sqrt(5)