# Paranormal Parabola?

Geometry Level 3

The equation of the parabola whose focus is $$\displaystyle \left( 1,-1 \right)$$ and vertex is $$\displaystyle \left( 2,1 \right)$$ can be written in the form $$\displaystyle a{ x }^{ 2 }+2hxy+{ by }^{ 2 }+2gx+2fy+c=0$$.

Find the value of $$\displaystyle Z$$, where $$\displaystyle Z=a+h+b+g+f+c$$.

Details And Assumption

• $$\displaystyle gcd\left( \left| a \right| \left| h \right| \left| b \right| \left| g \right| \left| f \right| \left| c \right| \right) =1$$

• Hint

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