What is x^2-4y^2-10x-40y-100=0 ?

The solution to x^2-4y^2-10x-40y-100=0 is Hyperbola with (h,k)=(5,-5),a=5,b= 5/2

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x^2-4y^2-10x-40y-100=0

x^{2} - 4 y^{2} - 10 x - 40 y - 100 = 0

(h, k) = (5, - 5), a = 5, b = \frac{5}{2}

Solution steps

x^{2} - 4 y^{2} - 10 x - 40 y - 100 = 0

Rewrite

x^{2} - 4 y^{2} - 10 x - 40 y - 100 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, - 5), a = 5, b = \frac{5}{2}

3 x^{2} + 6 x = 0.3 y^{2} - 6 y

x^{2} - y^{2} = 45

\frac{x ^{2}}{16} - \frac{y ^{2}}{81} = 1

x^{2} - 9 y^{2} + 8 x + 36 y - 29 = 0

7 y^{2} - 12 x^{2} = 84

What is x^2-4y^2-10x-40y-100=0 ?
The solution to x^2-4y^2-10x-40y-100=0 is Hyperbola with (h,k)=(5,-5),a=5,b= 5/2