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{x ^{2}}{0.0008} - \frac{y ^{2}}{0.999} = 1

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

x^{2} - 9 y^{2} = 144

- \frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1

19 x^{2} - 6 x - 22 y = 20 y^{2} + 7

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