Straight Line Question 334

Question: The equations of the lines through the point of intersection of the lines $ x-y+1=0 $ and $ 2x-3y+5=0 $ and whose distance from the point (3, 2) is $ \frac{7}{5}, $ is [IIT 1963]

Options:

A) $ 3x-4y-6=0 $ and $ 4x+3y+1=0 $

B) $ 3x-4y+6=0 $ and $ 4x-3y-1=0 $

C) $ 3x-4y+6=0 $ and $ 4x-3y+1=0 $

D)None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • Point of intersection is (2, 3). Therefore, the equation of line passing through (2, 3) is $ y-3=m(x-2) $ ??(i) or $ mx-y-(2m-3)=0 $ . According to the condition, $ \frac{3m-2-(2m-3)}{\sqrt{1+m^{2}}}=\frac{7}{5}\Rightarrow m=\frac{3}{4},\frac{4}{3} $ Hence the equations are $ 3x-4y+6=0 $ and $ 4x-3y+1=0 $ .