What is 9x^2-4y^2-90x-32y+125=0 ?

The solution to 9x^2-4y^2-90x-32y+125=0 is Hyperbola with (h,k)=(5,-4),a=2,b=3

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9x^2-4y^2-90x-32y+125=0

9 x^{2} - 4 y^{2} - 90 x - 32 y + 125 = 0

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

Solution steps

9 x^{2} - 4 y^{2} - 90 x - 32 y + 125 = 0

Rewrite

9 x^{2} - 4 y^{2} - 90 x - 32 y + 125 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{28}{x + y} + \frac{24}{x - y} = 6

4 x^{2} = 10 + y^{2}

x^{2} - 4 y^{2} - 18 x - 16 y - 35 = 0

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

y^{2} = 2 x^{2} - 3 x + 4

What is 9x^2-4y^2-90x-32y+125=0 ?
The solution to 9x^2-4y^2-90x-32y+125=0 is Hyperbola with (h,k)=(5,-4),a=2,b=3