What is 9y^2-16x^2-54y-32x-79=0 ?

The solution to 9y^2-16x^2-54y-32x-79=0 is Hyperbola with (h,k)=(-1,3),a=4,b=3

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9y^2-16x^2-54y-32x-79=0

9 y^{2} - 16 x^{2} - 54 y - 32 x - 79 = 0

(h, k) = (- 1, 3), a = 4, b = 3

Solution steps

9 y^{2} - 16 x^{2} - 54 y - 32 x - 79 = 0

Rewrite

9 y^{2} - 16 x^{2} - 54 y - 32 x - 79 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 3), a = 4, b = 3

\frac{40}{x + y} + \frac{2}{x - y} = 5

\frac{( y - 5 ) ^{2}}{15} - \frac{( x + 4 ) ^{2}}{49} = 1

y^{2} - 4 x^{2} - 24 x - 32 = 0

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

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

What is 9y^2-16x^2-54y-32x-79=0 ?
The solution to 9y^2-16x^2-54y-32x-79=0 is Hyperbola with (h,k)=(-1,3),a=4,b=3