What is 4x^2-y^2-4x-3=0 ?

The solution to 4x^2-y^2-4x-3=0 is Hyperbola with (h,k)=(1/2 ,0),a=1,b=2

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4x^2-y^2-4x-3=0

4 x^{2} - y^{2} - 4 x - 3 = 0

(h, k) = (\frac{1}{2}, 0), a = 1, b = 2

Solution steps

4 x^{2} - y^{2} - 4 x - 3 = 0

Rewrite

4 x^{2} - y^{2} - 4 x - 3 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = 1, b = 2

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

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

x = 1 - y^{2}

4 x^{2} + 9 y^{2} - 36 = 0

y = \frac{1}{4} x^{2}

What is 4x^2-y^2-4x-3=0 ?
The solution to 4x^2-y^2-4x-3=0 is Hyperbola with (h,k)=(1/2 ,0),a=1,b=2