# Orthogonal parabolas

Algebra Level 4

The two orthogonal parabolas $\begin{cases} y=(x+1)^2 \\ (y-2.5)^2=x+4 \end{cases}$ intersect at four distinct points, $$A=(x_1,y_1), B=(x_2, y_2)$$, $$C=(x_3, y_3)$$ and $$D=(x_4, y_4)$$. Let $$S=x_1+x_2+x_3+x_4$$ and $$R=y_1+y_2+y_3+y_4$$. Find the value of $$\lfloor{1000(R+S)}\rfloor$$.

Remark: If the orthogonal parabolas intersect at four distinct points, then these four points are always on a same circle.

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