The locus of a variable point which forms a triangle of fixed area with two fixed points is
- a circle
- a circle with fixed points as ends of a diameter
- a pair of non parallel lines
- a pair of parallel lines
Solution
Let $C$ be the variable point and $A ; B$ be two fixed points. Area of $\triangle \mathrm{ABC}=\frac{1}{2} \times \mathrm{AB} \times$ Height As $A B$ is fixed. So, for constant area height should remain same, which is only possible if C moves on a line parallel to $A B$ So, locus of C is a pair of parallel lines.
Asked in: AP EAMCET 2024 (22 May Shift 2)