AP EAMCET20226 Jul 2022Evening ShiftMathematicsStraight LinesActual
For the three points A(2,0), B(0,2) and P(1,1) , suppose d is the algebraic sum of the distances of A and B from a line that passes through P . Then, which of the following is correct?
Options
- Ad>0 for all lines
- Bd=0 for at least one line
- Cd=0 for all lines
- Dd>0 at least for one line
Correct answer
C. d=0 for all lines
Step-by-step solution
Let the variable line be a x+b y+c=0 The line passes through (1,1) , then a+b+c=0...(i) d= algebraic sum of distance from A and B to the line aligned d & = | 2 a+0 b+c a^2+b^2 |+ | 0 a+2 b+c a^2+b^2 | & = 2(a+b+c) 2 a^2+b^2 & =0 [ From Eq. (i)] aligned d=0, all the lines.