Question

find the equation of two straight lines which are parallel to the straight line x + 7 y + 2=0 and a unit distance from the point (2, - 1)​

Answer 1

Answer:
`x+7y+5(1+√(2))\ and\ x+7y+5(1-√(2))`

Step-by-step explanation:

General equation of line parallel to the given line x+7y+2=0 is

x+7y+c=0

This line must be unit distance from point (2,-1)

Point (2,-1) may be either side of line so we can write

`(\left | 2+7(-1)+c \right |)/(√(1^2+7^2))=1\\(\left | c-5 \right |)/(√(50))=1\\\left | c-5 \right |=√(50)\\c-5=\pm√(50)=\pm5√(2)\\c=5\pm5√(2)`

So, there can be 2 line i.e.

`x+7y+5(1+√(2))\ and\ x+7y+5(1-√(2))`