Geometric Constraints Math Example 3

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Example 3

easy
A point P(x,y)P(x, y) must satisfy: (1) it is in the first quadrant, and (2) its distance from the origin is at most 44. Write the constraints as inequalities.

Solution

  1. 1
    Step 1: First quadrant: x>0x > 0 and y>0y > 0.
  2. 2
    Step 2: Distance from origin ≤4\leq 4: x2+y2≤4\sqrt{x^2 + y^2} \leq 4, equivalently x2+y2≤16x^2 + y^2 \leq 16.

Answer

x>0x > 0, y>0y > 0, and x2+y2≤16x^2 + y^2 \leq 16.
Geometric constraints can be expressed as algebraic inequalities. The region satisfying all three constraints is the quarter-disk in the first quadrant with radius 44.

About Geometric Constraints

Conditions that limit or restrict the possible positions, sizes, or shapes of geometric objects in a problem.

Learn more about Geometric Constraints →

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