Implicit functions and Tangent lines

This tool will let you play around with tangent lines on a couple of curves that are defined implicitly. Try zooming in to convince yourself that our method of implicit differentiation to find a formula for the slope of these tangent lines makes sense. That is, by zooming in and forgetting the big picture, we actually can think of as a function of , allowing us to use our chain rule techniques to get an expression involving , which we can in fact solve for .