What is 6x^2-5y^2-24x+10y-11=0 ?

The solution to 6x^2-5y^2-24x+10y-11=0 is Hyperbola with (h,k)=(2,1),a=sqrt(5),b=sqrt(6)

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6x^2-5y^2-24x+10y-11=0

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

(h, k) = (2, 1), a = 5, b = 6

Solution steps

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

Rewrite

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 5, b = 6

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

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

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

2 xx - 3 yy = - 1214

3 x^{2} - 6 x - 4 y^{2} = 9

What is 6x^2-5y^2-24x+10y-11=0 ?
The solution to 6x^2-5y^2-24x+10y-11=0 is Hyperbola with (h,k)=(2,1),a=sqrt(5),b=sqrt(6)