Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0

Let the equation of line is,

Where m is the slope of the line

Since, this line passes through (4, 5), so it satisfy above equation,

Given lines are,

And,

Let m1 and m2 be the slope of given line (2) and (3) respectively. So,

And,

Since, equations of line (1) make equal angles with line (2) and (3). Therefore,

If slope of line (1) is -7/4, then equation of line (1) is,

And if slope of line is 4/7, then equation of line (1) is,

 

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