Question

Find the equation of the line parallel to 3x+4y+12=0 and passing at a distance 6 from the origin

Answer 1

Calculate the slope of the line 3x+4y+12=0
m = -a/b when equation is in the form ax+by+c=0
m= -3/4
Slope of the parallel lines are equal
y= (-3/4)x+c
3x+4y-4c=0
Distance from the origin is 6
|3(0)+4(0)-4c|/sqrt(3^2+4^2) =6
4c/5=6
4c=30
c=30/4
=15/2
y= (-3/4)x+15/2

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