# Coordinate geometry after reflection

Geometry Level 5

If the reflection of the curve $$xy=1$$ in the line $$y=2x$$ is

$$ax^2+bxy+cy^2+dx+ey+f=0$$,

Find value of $$\displaystyle{\left| a+b+c+d+e+f \right| }$$

Details and assumptions

$$\bullet$$ Here a,b,c,d,e,f are co-prime integers.

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