What is (a-b)(a+b)=2(3a-6) ?

The solution to (a-b)(a+b)=2(3a-6) is Hyperbola with (h,k)=(3,0),a=sqrt(3),b=sqrt(3)

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(a-b)(a+b)=2(3a-6)

(a - b) (a + b) = 2 (3 a - 6)

(h, k) = (3, 0), a = 3, b = 3

Solution steps

(a - b) (a + b) = 2 (3 a - 6)

Rewrite

(a - b) (a + b) - 2 (3 a - 6) = 0

in the form of a standard hyperbola equation

\frac{( b - 0 ) ^{2}}{( 3 ) ^{2}} - \frac{( a - 3 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 3, b = 3

\frac{( x - 0 ) ^{2}}{4 ^{2}} - \frac{( y - 0 ) ^{2}}{20 0 ^{2}} = 1

9 x^{2} - 4 y^{2} + 18 x + 32 y = 119

3 x^{2} - 3 y^{2} + 30 x - 6 y + 25 = 0

\frac{( x - 7 ) ^{2}}{a ^{2}} - \frac{( y + 6 ) ^{2}}{b ^{2}} = 1

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

What is (a-b)(a+b)=2(3a-6) ?
The solution to (a-b)(a+b)=2(3a-6) is Hyperbola with (h,k)=(3,0),a=sqrt(3),b=sqrt(3)