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Standard XII
Maths
Question
Let
P
be the point
(
1
,
0
)
and
Q
a point on the locus
y
2
=
8
x
. The locus of mid point of PQ 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
A
y
2
−
4
x
+
2
=
0
B
y
2
+
4
x
+
2
=
0
C
x
2
−
4
y
+
2
=
0
D
x
2
+
4
y
+
2
=
0
Open in App
Solution
Verified by Toppr
Given,
P
=
(
1
,
0
)
Let
Q
=
(
h
,
k
)
such that
k
2
=
8
h
(
α
,
β
)
be the mid points of
P
Q
α
=
h
+
1
2
,
β
=
k
+
0
2
[mid-point formula]
2
α
−
1
=
h
,
2
β
=
k
⇒
k
2
=
8
h
⇒
(
2
β
)
2
=
8
(
2
α
−
1
)
⇒
β
2
=
4
α
−
2
therefore, the locus of the midpoint of
P
Q
is
⇒
y
2
−
4
x
+
2
=
0
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