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 2021-03-05 Answered
A latus rectum of a conic section is a chord through a focus parallel to the directrix. Find the area bounded by the parabola y=x2/(4c) and its latus rectum.
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FieniChoonin
Answered 2021-03-06 Author has 102 answers
Step 1
It is known that the area bounded by the curves y=f(x)andy=g(x)on[a,b] is given by
A=ab (upper curve - lower curve) dx.
From the figure, the equation of latus rectum is y=c which is upper curve.
Note that the given graph is about y-axis.
Step 2
Substitute y=cy=x24c
and obtain that x=2x
Thus, the area bounded can be computed as follows.
A=202c (upper curve - lower curve) dx
=202c(cx24c)dx
=2[cxx312c]02c
=2[2c223c2]
=83c2
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