Question

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

• A. $3 x - 4 y - 6 = 0$ and $4 x + 3 y + 1 = 0$
• B. $3 x - 4 y + 6 = 0$ and $4 x - 3 y - 1 = 0$
• C. $3 x - 4 y + 6 = 0$ and $4 x - 3 y + 1 = 0$
• D. None of these

Answer 1

Answer: (C)

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

Answer 2

Point of intersection is (2, 3). Therefore, the equation of line passing through (2, 3) is

$y - 3 = m ( x - 2 )$ ……(i)

Or $m x - y - ( 2 m - 3 ) = 0$.

According to the condition,

$\frac { 3 m - 2 - ( 2 m - 3 ) } { \sqrt { 1 + m ^ { 2 } } } = \frac { 7 } { 5 } \Rightarrow m = \frac { 3 } { 4 } , \frac { 4 } { 3 }$

Hence the equations are $3 x - 4 y + 6 = 0$ and

$4 x - 3 y + 1 = 0$.