Equations to the two straight lines which pass through (4,5) and make equal angles with the two lines 3x = 4y + 7 and 5y = 12x + 6 - SL Loney, Coordinate geometry.

Ans. 9x - 7y = 1 and 7x + 9y = 73.

How did they get this?

as the question says that line is making equal angles with the two lines...

so the line is  the internal angular bisector and external angular bisector...

get the slopes of the angular bisector ..

as we know the point through which it is passing and the slope ,we can get the equation of the lines