What is 4x^2-9y^2+40x-72y-80=0 ?

The solution to 4x^2-9y^2+40x-72y-80=0 is Hyperbola with (h,k)=(-5,-4),a=3,b=2

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4x^2-9y^2+40x-72y-80=0

4 x^{2} - 9 y^{2} + 40 x - 72 y - 80 = 0

(h, k) = (- 5, - 4), a = 3, b = 2

Solution steps

4 x^{2} - 9 y^{2} + 40 x - 72 y - 80 = 0

Rewrite

4 x^{2} - 9 y^{2} + 40 x - 72 y - 80 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 5 ) ) ^{2}}{3 ^{2}} - \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 5, - 4), a = 3, b = 2

y^{2} = x^{2} - 9

36 x^{2} - 64 y^{2} - 504 x + 768 y - 1769 = 0

x^{2} - 4 x - y^{2} + 10 y + 5 = 0

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

(x - 3)^{2} - (y - 2)^{2} = 3

What is 4x^2-9y^2+40x-72y-80=0 ?
The solution to 4x^2-9y^2+40x-72y-80=0 is Hyperbola with (h,k)=(-5,-4),a=3,b=2