The sketch below shows the tangent line to the parabola [math]x^2=4py[/math]. First, you can move point [math]P[/math] anywhere on the parabola. Then show the Secant line. Adjust [math]h[/math] using the slider. Notice as [math]h\rightarrow0[/math], the secant line becomes the tangent line. Reinforcing what we learned in class, you can show the y-intercept of the tangent line. Notice, given that the tangent line at [math](x_1,y_1)[/math] will always go through [math](0,-y_1)[/math], we can also use these two points to determine the slope: [math]m=\frac{y_1-(-y_1)}{x_1-0}=\frac{2y_1}{x_1}[/math]