Question

if n is the length of perpendicular from point (3,-2) to the straight line L=12x-5y+6=0 and m is the distance of the line L=0 from 12x-5y-7=0,then

Answer 1

given info : if n is the length of perpendicular from point (3,-2) to the straight line L=12x-5y+6 = 0 and m is the distance of the line L = 0 from 12x-5y-7 = 0

To find : the value of m and n.

Solution : concept :

1. distance from the point A(p, q) to the line ax + by + c = 0 is given by, |ap + bq + c|/√(a² + b²)
2. Distance between two parallel lines ax + by + c = 0 and ax + by + k = 0 is given by, |c - k|/√(a² + b²)

Now using above concepts we can find the distance between them.

distance of point (3, -2) from line 12x - 5y + 6 = 0 is n = |12(3) - 5(-2) + 6|/√(12² + 5²)

= |36 + 10 + 6|/13

= 4

distance between lines 12x - 5y + 6 = 0 and 12x - 5y - 7 = 0 is m = |6 - (-7)|/√(12² + 5²)

= |6 + 7|/√169

= 13/13

= 1

Therefore the values of m and n are 1 and 4 respectively.