The distance between the lines `(x+7y)^2+4sqrt(2)(x+7y)-42=0` is_____________

Answer

2

Explanation

`(x+7y)=4sqrt(2)(x+7y)-42=0`
or `(x+7y)^(2)+7sqrt(2)(x+7y)-3sqrt(2)(x+7y)-42=0`
or `(x+7y)[x+7y+7sqrt(2)]-3sqrt(2)(x+7y+7sqrt(2))=0`
or `(x+7y+7sqrt(2))(x+7y-3sqrt(2))=0`
or `x+7y+7sqrt(2)=0andx+7y-3sqrt(2)=0`
or `d=|(7sqrt(2)+2sqrt(2))/(sqrt(1+49))|=(10sqrt(2))/(sqrt(50))=2`