use file() to read the file into an array.
use explode() to turn each line into an array so you can check for the values of name/email/url to find the line you want.
use unset() to erase that element form the array.
Use fopen() to re-open the file for writing.
write the file
be happy.
Note: this is NOT multi-user safe. Read about file locking to change that if you need to.