Focal chords A focal chord of a conic section is a line through a focus joining two points of the curve. The latus rectum is the focal chord perpendicular to the major axis of the conic. Prove the following properties.

The length of the latus rectum of the parabola y2 = 4px or x2 = 4py is 4.

Solution 90AE

Step 1:

A focal chord of a conic section is a line through a focus joining two points of the curve. The latus rectum is the focal chord perpendicular to the major axis of the conic

The objective is to prove The length of the latus rectum of the parabola

Step 2:

Four standard forms of the parabola are = 4ax ; = − 4ax ; = 4ay ; = − 4ay

We know that for = 4ax length of latus rectum is 4a