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

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

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

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

(h, k) = (0, 0), a = 2, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{2 ^{2}} - \frac{( x - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2, b = 5

\frac{x ^{2}}{81} - \frac{y ^{2}}{49} = 1

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

(a + b) \cdot (a - b) = 20

y^{2} - 2 x^{2} + 6 y - 16 x - 31 = 0

y^{2} = x^{2} - 3

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