What is 6x^2-8y^2-108x-64y=-310 ?

The solution to 6x^2-8y^2-108x-64y=-310 is Hyperbola with (h,k)=(9,-4),a=2sqrt(2),b=sqrt(6)

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6x^2-8y^2-108x-64y=-310

6 x^{2} - 8 y^{2} - 108 x - 64 y = - 310

(h, k) = (9, - 4), a = 22, b = 6

Solution steps

6 x^{2} - 8 y^{2} - 108 x - 64 y = - 310

Rewrite

6 x^{2} - 8 y^{2} - 108 x - 64 y = - 310

in the form of a standard hyperbola equation

\frac{( x - 9 ) ^{2}}{( 2 2 ) ^{2}} - \frac{( y - ( - 4 ) ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (9, - 4), a = 22, b = 6

\frac{( a - b )}{a ^{2} - 2 ab + b ^{2}} - \frac{3}{a - b} = a + b

9 (X^{2} + 6 X) - 4 Y^{2} = - 45

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(x - 3) (x + 1) = yy

x^{2} - 25 y^{2} = 25

What is 6x^2-8y^2-108x-64y=-310 ?
The solution to 6x^2-8y^2-108x-64y=-310 is Hyperbola with (h,k)=(9,-4),a=2sqrt(2),b=sqrt(6)