What is y^2=x^2+12x+32 ?

The solution to y^2=x^2+12x+32 is Hyperbola with (h,k)=(-6,0),a=2,b=2

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y^2=x^2+12x+32

y^{2} = x^{2} + 12 x + 32

(h, k) = (- 6, 0), a = 2, b = 2

Solution steps

y^{2} = x^{2} + 12 x + 32

Rewrite

y^{2} = x^{2} + 12 x + 32

in the form of a standard hyperbola equation

\frac{( x - ( - 6 ) ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 6, 0), a = 2, b = 2

- \frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{7} = 1

(x - 2 \cdot y) \cdot (x + 2 \cdot y) = 90005

x^{2} - y^{2} = 303

\frac{( y + 3 ) ^{2}}{4} - (x - 1)^{2} = 1

(\frac{x + 2}{10})^{2} - (\frac{y + 4}{25})^{2} = 1

What is y^2=x^2+12x+32 ?
The solution to y^2=x^2+12x+32 is Hyperbola with (h,k)=(-6,0),a=2,b=2