Obtain the coordinates of the feet of the perpendiculars drawn from the origin upon the lines 3x - 5y + 2 = 0 and 4x - 3y + 5 = 0 and show that the equation of the straight line joining these feet is 26x + 53y = 11.

please help me how to solve it.

To find feet of perpendiculars you need to learn a formula-
feet of point (x₁,y₁) in line ax+by+c=0 is (-ar+x₁,-br+y₁) where r=(ax₁+by₁+c)/a²+b²
so in this question point is origin in case of line 3x-5y+2=0 a=3,b=-5,c=2 and r=2/34=1/17
and foot is (-3/17,5/17) and for line 4x-3y+5=0 foot is (-4/5,3/5) and equation of line passing through them is 26x+53y=11