Obtain the coordinate of the foot of perpendiculars drawn from the origin to the lines 3x-5y+2=0 and 4x-3y+5=0 and show the equation of the set of all points
Answers
Given : foot of perpendiculars drawn from the origin to the lines 3x-5y+2=0 and 4x-3y+5=0
To Find : equation and foot point
Solution:
3x-5y+2=0
=> 5y = 3x + 2
=> y = 3x/5 + 2/5
=> slope = 3/5
Slope of perpendicular line
= - 5/3
perpendicular from origin
=> y = -5/3 x
=> 3y = - 5x
=> 5x + 3y = 0
5y = 3x + 2
Solving 25x + 15y = 0 , 15y = 9x + 6
y= 10/34 = 5/17
x = -6/34 = -3/17
(-3/17 , 5/17) -foot of perpendicular on 3x-5y+2=0
4x-3y+5=0
=> 3y = 4x + 5
slope = 4/3
Slope of perpendicular foot = -3/4
y = -3/4 x
=>4y = - 3x
=> 3x + 4y = 0
3y = 4x + 5
y = 15/25 = 3/5
x = -20/25 = -4/5
( -4/5 , 3/5)
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