 
We will show where the formula for the length of the latus rectum comes from, for a horizontal ellipse centred at (0, 0). The latus rectum in this case is a vertical line at the focus, and is at a distance c from the centre. This makes the point at the top of the latus rectum on the ellipse the point (c, y). In order to find the length of the latus rectum, we are going to find the value of y at that point, and then double it. Here is the derivation: 
We start with the equation of the ellipse. Clearing fractions. Solving for y. Factoring out b2. Filling in the value of x at the point (c, y). Replacing a2 - c2 by b2 The three values are related by the Pythagorean Theorem. Finding the square root of both sides. |