of the focus of the parabola divides the focal chord of the parabola in segments 3 and 2 the length of the latus rectum is
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Step-by-step explanation:
Let s(a,o) be the focus of the given parabola
Let the end points of the focal chord be P(at
2
,2at)andQ(
t
2
a
,
t
−2a
)
SP and SQ are segments of the focal chord with length b and c respectively
therefore, b=3 and c=2
also, SP=
(a−at)
2
+4a
2
t
2
=a(1+t
2
)
SQ=
(a−
t
2
a
)
2
+
t
2
4a
2
=a(
t
2
t
2
+1
)
Now we have,
SP
1
+
SQ
1
=
a(1+t
2
)
1
+
a(1+t
2
)
t
2
=
a
1
⇒
b
1
+
c
1
=
a
1
⇒
3
1
+
2
1
=
a
1
⇒a=
5
6
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