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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 21
Total: 71
Let
P
be the point
(
1
,
0
)
and
Q
a point on the parabola
y
2
=
8
x
. The locus of mid point of
P
Q
is
y
2
−
4
x
+
2
=
0
y
2
+
4
x
+
2
=
0
x
2
+
4
y
+
2
=
0
x
2
−
4
y
+
2
=
0
Validate
Solution:
P
=
(
1
,
0
)
Q
=
(
h
,
k
)
Such that
k
2
=
8
h
Let
(
α
,
β
)
be the midpoint of
P
Q
α
=
h
+
1
2
,
β
=
k
+
0
2
∴
2
α
−
1
=
h
2
β
=
k
(
2
β
)
2
=
8
(
2
α
−
1
)
⇒
β
2
=
4
α
−
2
⇒
y
2
−
4
x
+
2
=
0
© examsnet.com
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