What is 5x^2-4y^2-20x+8y-4=0 ?

The solution to 5x^2-4y^2-20x+8y-4=0 is Hyperbola with (h,k)=(2,1),a=2,b=sqrt(5)

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5x^2-4y^2-20x+8y-4=0

5 x^{2} - 4 y^{2} - 20 x + 8 y - 4 = 0

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

Solution steps

5 x^{2} - 4 y^{2} - 20 x + 8 y - 4 = 0

Rewrite

5 x^{2} - 4 y^{2} - 20 x + 8 y - 4 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y - 1 ) ^{2}}{25} - \frac{( x + 2 ) ^{2}}{9} = 1

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

x^{2} - 5 y^{2} = 25

\frac{y ^{2}}{100} - \frac{x ^{2}}{36} = 1

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

What is 5x^2-4y^2-20x+8y-4=0 ?
The solution to 5x^2-4y^2-20x+8y-4=0 is Hyperbola with (h,k)=(2,1),a=2,b=sqrt(5)