The question uses vector operations (dot products, vector sums) involving points on a conic, foci, or origin to derive a geometric or algebraic result.
Let the parabola $C : y ^ { 2 } = 4 x$ have focus $F$. A line through $( - 2,0 )$ with slope $\frac { 2 } { 3 }$ intersects $C$ at points $M$ and $N$. Then $\overrightarrow { F M } \cdot \overrightarrow { F N } =$