What is 4x^2-y^2+12x+5=0 ?

The solution to 4x^2-y^2+12x+5=0 is Hyperbola with (h,k)=(-3/2 ,0),a=1,b=2

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4x^2-y^2+12x+5=0

4 x^{2} - y^{2} + 12 x + 5 = 0

(h, k) = (- \frac{3}{2}, 0), a = 1, b = 2

Solution steps

4 x^{2} - y^{2} + 12 x + 5 = 0

Rewrite

4 x^{2} - y^{2} + 12 x + 5 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{1 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{3}{2}, 0), a = 1, b = 2

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

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

12 x^{2} - 4 y^{2} = 96

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

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

What is 4x^2-y^2+12x+5=0 ?
The solution to 4x^2-y^2+12x+5=0 is Hyperbola with (h,k)=(-3/2 ,0),a=1,b=2