What is the shortest path equation between 2 points on the surface of $z = xy$?

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Given two points on the surface $z=xy$, $A=(x_0,y_0)$, $B=(x_1,y_1)$. How to present the shortest path between $A$ and $B$? I haven't learn about differential geometry, but I know about Calculus and Linear Algebra. Looking forward for help!
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