HKDSE Mathematics Question Review (20240709)

Question:

Consider linear programming. Why should we take extrema from the edges?

Solution:

The required solution should be only one. If we take the coordinates from an edgeless line, we will have infinite solutions, which is a contradiction.

Further question

Given a circle in a Cartesian coordinate plane. By using a linear constraint, describe how we can get the required solution.

Solution:

The constraint should be a tangent to circle which meets the circle only once.

2 parallel tangents should be formed, in which only one of them is the required solution.