What is x^2-25y^2-14x+100y-76=0 ?

The solution to x^2-25y^2-14x+100y-76=0 is Hyperbola with (h,k)=(7,2),a=5,b=1

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x^2-25y^2-14x+100y-76=0

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

(h, k) = (7, 2), a = 5, b = 1

Solution steps

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

Rewrite

x^{2} - 25 y^{2} - 14 x + 100 y - 76 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (7, 2), a = 5, b = 1

- x^{2} + 4 y^{2} - 1 = 0

\frac{( y - 4 ) ^{2}}{36} - x^{2} = 1

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

(x - y - 3) \cdot (x + y + 3) = 16

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

What is x^2-25y^2-14x+100y-76=0 ?
The solution to x^2-25y^2-14x+100y-76=0 is Hyperbola with (h,k)=(7,2),a=5,b=1