Find the equation of the line passing through the inersection of lines x-y+1=0 and 2x-3y+5=0 and whose distance from the point (3,2) is 7/5.

Hello Student, Please find the solution

Here you can use the concept of family of lines
The equation of the line passing through the inersection of lines x-y+1=0 and 2x-3y+5=0 can be assumed as

Now the distance of this line from (3,2) is 7/5
so,

Solve the above equation and find out
Once you get , put it back in equation

And you will get the final answer