Parabola: Latus Rectum
How to find the latus rectum of a parabola: formula, 3 examples, and their solutions.
Formulay2 = 4px
The latus rectum of a parabola is a segment
that passes through the focus
and that is parallel to the directrix.
(brown segment)
Parabola: Equation
For the parabola y2 = 4px,
the length of the latus rectum is
|4p|.
Exampley2 = 8x
Solution
Solution (Detail)
Exampley2 = -12x
Solution
Solution (Detail)
y2 = -12x
Then the latus rectum is
|-12|.
|-12| = 12
So 12 is the answer.
Formulax2 = 4py
For the parabola x2 = 4py,
the length of the latus rectum is
|4p|.
Exampley = 3x2
Solution
Solution (Detail)
Switch both sides.
Divide both sides by 3.
Then x2 = [1/3]y.
x2 = [1/3]y
Then the latus rectum is
|1/3|.
|1/3| = 1/3
So 1/3 is the answer.