What is 81x^2-64y^2+1134x-640y-2815=0 ?

The solution to 81x^2-64y^2+1134x-640y-2815=0 is Hyperbola with (h,k)=(-7,-5),a=8,b=9

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81x^2-64y^2+1134x-640y-2815=0

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

(h, k) = (- 7, - 5), a = 8, b = 9

Solution steps

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

Rewrite

81 x^{2} - 64 y^{2} + 1134 x - 640 y - 2815 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 7 ) ) ^{2}}{8 ^{2}} - \frac{( y - ( - 5 ) ) ^{2}}{9 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 7, - 5), a = 8, b = 9

\frac{y ^{2}}{3} - \frac{x ^{2}}{16} = 1

2500 x^{2} - 640 x + 41 = y^{2}

5 x^{2} - 3 y^{2} + 31 x + 23 y + 24 = 0

y^{2} = \frac{( 900 + 36 ( x - 8 ) ^{2} )}{25}

\frac{x ^{2}}{400} - \frac{y ^{2}}{625} = 1

What is 81x^2-64y^2+1134x-640y-2815=0 ?
The solution to 81x^2-64y^2+1134x-640y-2815=0 is Hyperbola with (h,k)=(-7,-5),a=8,b=9