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Test Index
JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 48
Total: 100
The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points
(
a
2
+
1
,
a
2
+
1
)
and
(
2
a
,
−
2
a
)
,
a
≠
0
. Then for anya, the orthocentre of this triangle lies on the line:
[Online April 11, 2015]
y
−
2
a
x
=
0
y
−
(
a
2
+
1
)
x
=
0
y
+
x
=
0
(
a
−
1
)
2
x
−
(
a
+
1
)
2
y
=
0
Validate
Solution:
Circumcentre
=
(
0
,
0
)
Centroid
=
(
(
a
+
1
)
2
2
,
(
a
−
1
)
2
2
)
We know the circumcentre (O),
Centroid
(
G
)
and orthocentre
(
H
)
of a triangle lie on the line joining the
O
and
G
.
Also,
H
G
G
O
=
2
1
⇒
Coordinate of orthocentre
=
3
(
a
+
1
)
2
2
,
3
(
a
−
1
)
2
2
Now, these coordinates satisfies eqn given in option (d) Hence, required eqn of line is
(
a
−
1
)
2
x
−
(
a
+
1
)
2
y
=
0
© examsnet.com
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