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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.

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.

Grade:11

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
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

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