What is 4x^2-8x-9y^2-72y+112=0 ?

The solution to 4x^2-8x-9y^2-72y+112=0 is Hyperbola with (h,k)=(1,-4),a=2sqrt(7),b=3sqrt(7)

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4x^2-8x-9y^2-72y+112=0

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0

(h, k) = (1, - 4), a = 27, b = 37

Solution steps

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0

Rewrite

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 2 7 ) ^{2}} - \frac{( x - 1 ) ^{2}}{( 3 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 4), a = 27, b = 37

y^{2} = 4 0^{2} + x^{2}

x^{2} - 3 y^{2} - 8 x + 18 y - 14 = 0

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

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

16 y^{2} - 4 x^{2} + 16 x - 80 = 20

What is 4x^2-8x-9y^2-72y+112=0 ?
The solution to 4x^2-8x-9y^2-72y+112=0 is Hyperbola with (h,k)=(1,-4),a=2sqrt(7),b=3sqrt(7)