What is 4x^2-9y^2-48x+108=0 ?

The solution to 4x^2-9y^2-48x+108=0 is Hyperbola with (h,k)=(6,0),a=3,b=2

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4x^2-9y^2-48x+108=0

4 x^{2} - 9 y^{2} - 48 x + 108 = 0

(h, k) = (6, 0), a = 3, b = 2

Solution steps

4 x^{2} - 9 y^{2} - 48 x + 108 = 0

Rewrite

4 x^{2} - 9 y^{2} - 48 x + 108 = 0

in the form of a standard hyperbola equation

\frac{( x - 6 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (6, 0), a = 3, b = 2

\frac{( x - 9 ) ^{2}}{9} - \frac{( y + 4 ) ^{2}}{25} = 1

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

\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

What is 4x^2-9y^2-48x+108=0 ?
The solution to 4x^2-9y^2-48x+108=0 is Hyperbola with (h,k)=(6,0),a=3,b=2