What is 9y^2-16x^2-256=0 ?

The solution to 9y^2-16x^2-256=0 is Hyperbola with (h,k)=(0,0),a= 16/3 ,b=4

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9y^2-16x^2-256=0

9 y^{2} - 16 x^{2} - 256 = 0

(h, k) = (0, 0), a = \frac{16}{3}, b = 4

Solution steps

9 y^{2} - 16 x^{2} - 256 = 0

Rewrite

9 y^{2} - 16 x^{2} - 256 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{16}{3} ) ^{2}} - \frac{( x - 0 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{16}{3}, b = 4

\frac{x ^{2}}{25} - \frac{y ^{2}}{36} = 1

- x^{2} - 6 x + y - 8 = 0

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

x = - \frac{1}{12} y^{2}

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

What is 9y^2-16x^2-256=0 ?
The solution to 9y^2-16x^2-256=0 is Hyperbola with (h,k)=(0,0),a= 16/3 ,b=4