Tangent Line to an Ellipse - Motivation for Implicit DifferentiationIt is easy to draw the tangent line to the ellipse 3x² + 4y² = 12, so we should be able to find the slope at of the line, and thus the slope of the graph, at a point, like (1,1.5). Clearly y is not a function of x. (It fails the vertical line test.) So how do we find dy/dx? Drag the blue point around the ellipse and see how the slope changes. What happens at (2,0) and (-2,0)? What is the tangent line at those points? Jason McCullough, October 5, 2009, Created with GeoGebra |