Suppose that . Find the least distance from the point [tex](a,0) to the ellipse .

Well basically i used the distance formula, so .

Then i set up a function .

I differentiated it it find .

I then found to be the minimum turning point and subbed it back into distance formula to get .

However the answer is:

least distance

i get why its |a-2| if a>2 but i dont get why its |a-2| between a=3/2 and a=2.

Can someone please explain why?