find the equation of straight lines which are perpendicular to the line 12x + 5y = 17 and at - Maths - Straight Lines

Question

find the equation of straight lines which are perpendicular to the
line 12x + 5y = 17 and at a distance of 2 units from point v(-4,1 )

Ajanta Trivedi · Accepted Answer

the equation of the given line
is 12x+5y=17
slope of the line =
-12/5
slope of the line which is
perpendicular to the given line is 5/12
let the equation of the required line is
y=512x+c12y=5x+12c⇒5x-12y+12c=0 
(2)now if the perpendicular distance of the line (2) from point (-4,1) is 2 units5*(-4)-12*1+12c52+122=2-20-12+12c169=2-32+12c13=2
-32+12c13=±2-32+12c=±2612c=32±26⇒12c=32+26 or 12c=32-2612c=58 or 12c=6
thus the equations of the required lines are
12y=5x+58 or 12y=5x+6

hope this helps you

find the equation of straight lines which are perpendicular to the line 12x + 5y = 17 and at a distance of 2 units from point v(-4,1 )