What is 5x^2-4y^2-20x+24y-36=0 ?

The solution to 5x^2-4y^2-20x+24y-36=0 is Hyperbola with (h,k)=(2,3),a=2,b=sqrt(5)

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5x^2-4y^2-20x+24y-36=0

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

(h, k) = (2, 3), a = 2, b = 5

Solution steps

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

Rewrite

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = 2, b = 5

x^{2} - 2 x + 1 = 2 k (x) (k (x) - 2)

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

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

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

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

What is 5x^2-4y^2-20x+24y-36=0 ?
The solution to 5x^2-4y^2-20x+24y-36=0 is Hyperbola with (h,k)=(2,3),a=2,b=sqrt(5)