MCQ
If the point $(x, y)$ be equidistant from the points $(a + b,\,b - a)$ and $(a - b,\,a + b),$ then
- A$ax + by = 0$
- B$ax - by = 0$
- C$bx + ay = 0$
- ✓$bx - ay = 0$
$ \Rightarrow \,\,{x^2} + {(a + b)^2} - 2x\,(a + b) + {y^2} + {(b - a)^2} - 2y(b - a)$
$ = {x^2} + {(a - b)^2} - 2x(a - b) + {y^2} + {(a + b)^2} - 2y(a + b)$
On simplification, we get $bx - ay = 0$
Trick : The locus will be right bisector of the line joining the given points, therefore the line must pass through the mid-points of the given point i.e. $(a, b)$. Obviously, the line given in option $(d)$ passes through $(a, b)$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.