2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Straight Line

JEE Main & Advanced Mathematics Straight Line Question Bank Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line

  • question_answer
    The point on the line \[x+y=4\]which lie at a unit distance from the line \[4x+3y=10\], are                     [IIT 1976]

    A)            \[(3,\,1),(-7,\,11)\]                    

    B)            \[(3,\,1),(7,\,11)\]

    C)            \[(-3,\,1),(-7,\,11)\]                   

    D)            \[(1,\,3),(-7,\,11)\]

    Correct Answer: A

    Solution :

               Let the point  (h, k) then \[h+k=4\]                        ..?(i)                    and \[1=\pm \frac{4h+3k-10}{\sqrt{{{4}^{2}}+{{3}^{2}}}}\Rightarrow 4h+3k=15\] ?..(ii)                    and \[4h+3k=5\]                                                               ?..(iii)                    On solving (i) and (ii); and (i) and (iii), we get the required points (3, 1) and (?7, 11).               Trick: Check with options. Obviously, points (3, 1) and (-7, 11) lie on \[x+y=4\]and perpendicular distance of these points from \[4x+3y=10\]is 1.


You need to login to perform this action.
You will be redirected in 3 sec spinner