## Two focal tangents meet on the directrix at 90°

This parabola can be drawn in several ways:

**x = y²/4**, or **y² = 4x**, or parametrically **x = t²/4, y = t**

and the directrix **x = -1**. Enter a point at the focus **(1, 0)** , and another on the curve, labelled **‘A’**. Construct a tangent through A. construct a straight line through A and the Focus, and find its other intersection (‘B’) with the parabola (use ‘Add point’ with Ctrl). Double-click on ‘B’ to establish its association with the parabola, then draw a tangent through ‘B’. Find the intersection of the two tangents, and display the angle (make sure you are in degrees).

Move ‘A’ around to domstrate that the two tangents meet on the directrix at 90°.

CAREFUL: If the second intersection, ‘B’, goes off the page, it can get lost and the construction collapses. If that happens there is always CTRL-Z (Command Z on Mac) to get you out of jail! (Undo)

Download Autograph files: parabola (parametric), and parabola2 (cartesian)

In each file, an ANIMATION is set up to demonstrate this.

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