Shows how to construct the complex points on a parabola in a particular iplane using tangents. Drag the slider marked t to see the construction progress in the following steps:

Draw a vertical line from P to the parabola and mark the point on the parabola. Let's call it A.

Draw the tangent to the parabola at the point A.

Copy the distance from A to P inside the parabola from A. Let's call this new point B.

Draw a line through B parallel to the tangent at A and mark where it meets the parabola. Let's call these points C and D.

Draw vertical lines through C and D.

Draw a line through P parallel to the tangent at A. Mark where it meets the vertical lines through C and D.

These final two points are the real images of the complex points on the parabola in the iplane at P.