Latus rectum of the parabola:

Notes:

• Any chord of parabola y² = 4ax which is perpendicular to its axis is called as double ordinate.
• Two parabolas are said to be equal when their latus recta are equal.

Illustration: Find out the equation of parabola whose focus is (1, - 1), and whose vertex is (2, 1). Also find equation of the axis and latus rectum.

Solution: As we know that vertex is the midpoint of focus and point of intersection of directrix with the axis so point P(h, k) is       

                              ∴equation of directrix y - 3 = -1/2 (x - 3) => x + 2y = 9

                              ∴ equation of parabola is (x - 1)² + (y + 1)² =  

                              equation of latus rectum

                              y + 1 = 1/2 (x - 1) => x + 2y + 1 = 0 

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