What is 4x^2-9y^2-48x-72y+108=0 ?

The solution to 4x^2-9y^2-48x-72y+108=0 is Hyperbola with (h,k)=(6,-4),a=2sqrt(3),b=3sqrt(3)

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4x^2-9y^2-48x-72y+108=0

4 x^{2} - 9 y^{2} - 48 x - 72 y + 108 = 0

(h, k) = (6, - 4), a = 23, b = 33

Solution steps

4 x^{2} - 9 y^{2} - 48 x - 72 y + 108 = 0

Rewrite

4 x^{2} - 9 y^{2} - 48 x - 72 y + 108 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 2 3 ) ^{2}} - \frac{( x - 6 ) ^{2}}{( 3 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (6, - 4), a = 23, b = 33

9 x^{2} - 4 y^{2} - 40 y - 136 = 0

4 x^{2} - y^{2} - 8 x - 4 y - 4 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

x^{2} - y^{2} = 105

x^{2} - y^{2} - (- 10) = 0

What is 4x^2-9y^2-48x-72y+108=0 ?
The solution to 4x^2-9y^2-48x-72y+108=0 is Hyperbola with (h,k)=(6,-4),a=2sqrt(3),b=3sqrt(3)