What is 16x^2-128x-9y^2+36y+76=0 ?

The solution to 16x^2-128x-9y^2+36y+76=0 is Hyperbola with (h,k)=(4,2),a=3,b=4

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16x^2-128x-9y^2+36y+76=0

16 x^{2} - 128 x - 9 y^{2} + 36 y + 76 = 0

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

Solution steps

16 x^{2} - 128 x - 9 y^{2} + 36 y + 76 = 0

Rewrite

16 x^{2} - 128 x - 9 y^{2} + 36 y + 76 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{9} - \frac{y ^{2}}{8} = 1

x^{2} - y^{2} - 5 x - 20 y + 25 = 0

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

96 + 32 x + 16 x^{2} - 16 y^{2} = 0

- 4 x^{2} + y^{2} - 16 x - 52 = 0

What is 16x^2-128x-9y^2+36y+76=0 ?
The solution to 16x^2-128x-9y^2+36y+76=0 is Hyperbola with (h,k)=(4,2),a=3,b=4