Question

Find the equation of the line parallel to 3x-4y-5=0 at a unit distance from it

Answer 1

Answer: 3x-4y = 0 and 3x-4y-10=0.

Step-by-step explanation:

Equation of line parallel to any given line ax + by + c = 0 will always be in the form ax + by + c' = 0, only the contant would change.

So, equation of the line parallel to 3x-4y-5 = 0 will be of form 3x-4y+c=0.

Distance between 2 given parallel lines ax+by+c=0 and ax+by+c'=0 is given by      |c-c'|/√a²+b².

Thus, |c+5|/√3²+4² = 1

=>|c+5|/5 = 1

=>|c+5| = 5

=> c+5 = ±5

=>c = 0 or - 10.

Thus, there are 2 parallel lines at a unit distance from the given equation:

3x-4y = 0 and 3x-4y-10=0.