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,b= 5/2

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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 = 5, b = \frac{5}{2}

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

Therefore Hyperbola properties are:

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

\frac{9 y ^{2}}{36} - \frac{4 x ^{2}}{36} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{5} = 1

x^{2} + (5 - 6) y^{2} = 1

x^{2} + 11 = y^{2} + 4 x - 2 y

\frac{( x - 1 ) ^{2}}{4} - \frac{y ^{2}}{5} = 1

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,b= 5/2