A latus rectum of a conic section is a chord through a focus parallel to the directrix. Find the area bounded by the parabola displaystyle{y}={x}^{2}text{/}{left({4}{c}right)} and its latus rectum.
preprekomW 2021-03-05Answered
A latus rectum of a conic section is a chord through a focus parallel to the directrix. Find the area bounded by the parabola and its latus rectum.
Step 1
It is known that the area bounded by the curves is given by
(upper curve - lower curve) dx.
From the figure, the equation of latus rectum is which is upper curve.
Note that the given graph is about y-axis.
Step 2
Substitute
and obtain that
Thus, the area bounded can be computed as follows.
(upper curve - lower curve) dx