What is 4x^2-y^2-20x-10y-25=0 ?

The solution to 4x^2-y^2-20x-10y-25=0 is Hyperbola with (h,k)=(5/2 ,-5),a= 5/2 ,b=5

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4x^2-y^2-20x-10y-25=0

4 x^{2} - y^{2} - 20 x - 10 y - 25 = 0

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

Solution steps

4 x^{2} - y^{2} - 20 x - 10 y - 25 = 0

Rewrite

4 x^{2} - y^{2} - 20 x - 10 y - 25 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

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

3 y^{2} - x^{2} + 18 y + 4 x + 28 = 0

\frac{50}{x + y} + \frac{8}{x - y} = 7

4 x^{2} - 9 y^{2} - 16 x + 36 y = 56

What is 4x^2-y^2-20x-10y-25=0 ?
The solution to 4x^2-y^2-20x-10y-25=0 is Hyperbola with (h,k)=(5/2 ,-5),a= 5/2 ,b=5