A person standing at the junction (crossing) of two straight paths represented by the equations `2x - 3y + 4 = 0` and `3x + 4y -5=0` wants to reach the path whose equation is `6x - 7y + 8 = 0` in the least time. Find equation of the path that he should follow.

Explanation

given a person is standing at the junction of the below lines

`2x−3y+4=0 ...(1) `

`3x+4y−5=0 ...(2)`

Solving equation (1) and (2) ,we get

`x=−1/(17)​ and y=(22​)/(17)`

So, the person is standing at point `(−(1/(17)​,(22)/(17))​)`

Given equation of path is

`6x−7y+8=0 ...(3)`

...