What is 10x^2-64y^2-140x+768y-2454=0 ?

The solution to 10x^2-64y^2-140x+768y-2454=0 is Hyperbola with (h,k)=(7,6),a=8,b=sqrt(10)

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10x^2-64y^2-140x+768y-2454=0

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2454 = 0

(h, k) = (7, 6), a = 8, b = 10

Solution steps

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2454 = 0

Rewrite

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2454 = 0

in the form of a standard hyperbola equation

\frac{( x - 7 ) ^{2}}{8 ^{2}} - \frac{( y - 6 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (7, 6), a = 8, b = 10

y^{2} - 16 x^{2} = 1

\frac{( y - 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

x^{2} - y^{2} - 4 x - 6 y = 0

(3 x - 3)^{2} - (2 y - 4)^{2} = 68

64 x^{2} - 100 y^{2} = 6400

What is 10x^2-64y^2-140x+768y-2454=0 ?
The solution to 10x^2-64y^2-140x+768y-2454=0 is Hyperbola with (h,k)=(7,6),a=8,b=sqrt(10)