What is 4y^2=x^2-4x ?

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

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4y^2=x^2-4x

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

(h, k) = (2, 0), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 0), a = 2, b = 1

x^{2} = 4 + 3 y^{2}

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

(y + 1)^{2} = 4 + x^{2}

\frac{( x + 4 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{16} = 1

- 64 x^{2} + 25 y^{2} - 1152 x - 350 y - 5559 = 0

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