with the sentence where is your mother. איפה האמה שלך was marked as having a typo the article ה prior to the word אמא. But, where is my orange need the article ה. I don't understand how these to sentences differ.
The word אמא is already "the mother". If you say האמא it would be "the the mother"
לאן = to where, as in where are you going to
איפה = where, as in where are my keys