What is 9y^2-16x^2-90y-128x-175=0 ?

The solution to 9y^2-16x^2-90y-128x-175=0 is Hyperbola with (h,k)=(-4,5),a=4,b=3

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9y^2-16x^2-90y-128x-175=0

9 y^{2} - 16 x^{2} - 90 y - 128 x - 175 = 0

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

Solution steps

9 y^{2} - 16 x^{2} - 90 y - 128 x - 175 = 0

Rewrite

9 y^{2} - 16 x^{2} - 90 y - 128 x - 175 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 1 y^{2} = 88

\frac{x ^{2}}{64} - \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{8} = 1

(x + 3)^{2} - y^{2} = 159

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

What is 9y^2-16x^2-90y-128x-175=0 ?
The solution to 9y^2-16x^2-90y-128x-175=0 is Hyperbola with (h,k)=(-4,5),a=4,b=3