Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines
Paragraph: Read the following write up carefully and answer the following questions: If (x₁, y₁ ) is the image (reflection) of the point (x, y) in the line y=m x , then x ₁= 1- m ^2 1+ m ^2 x + 2 ~m 1+ m ^2 y and y ₁= 2 ~m 1+ m ^2 x + m ^2-1 1+ m ^2 y [ array l x₁ y₁ array ]= [ array cc 1-m^2 1+m^2 & 2 m 1+m^2 2 m 1+m^2 & m^2-1 1+m^2 array ] [ array l x y array ] X₁=A X X=A⁻¹ X₁ [ array l x y array ]= [ array cc 1-m^
Options
- Ap x-q y=1
- Bp x-q y=1-q
- Cp x-q y=1-6 q
- Dp x-q y=1-4 q
Correct answer
C. p x-q y=1-6 q
Step-by-step solution
Shift the origin to the point (0,3) so that any point (x₁, y₁ ) on the reflected line is given by aligned & [ array c x₁ y₁-3 array ]= [ array cc 1 & 0 0 & -1 array ] [ array c 1-q(h+3) p h array ]( since m=0) & x₁= 1-q(h+3) p , y₁-3=-h p x₁=q y₁+1-6 q aligned and hence the reflected line is p x-q y=1-6 q .