Drag point A around the curve to see how the tangent changes.
To enable trace, right click point B and select trace.

What is the equation of the curve?
What is the relationship between point A and point B?
What is the relationship between the gradient of the curve at point A and point B?
After you have turned trace on, drag point A around the curve again. What do you notice?
What is the equation of the new curve?
Can you spot a relationship between the new curve and the original?