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JEE Main 9 Apr 2024 Shift 2 Solved Paper
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© examsnet.com
Question : 7
Total: 90
Two vertices of a triangle
ABC
are
A
(
3
,
−
1
)
and B
(
−
2
,
3
)
, and its orthocentre is
P
(
1
,
1
)
. If the coordinates of the point
C
are
(
α
,
β
)
and the centre of the circle circumscribing the triangle
PAB
is (
h
,
k
), then the value of
(
α
+
β
)
+
2
(
h
+
k
)
equals :
[9 Apr 2024 Shift 2]
51
81
5
15
Validate
Solution:
👈: Video Solution
M
AB
=
4
−
5
⇒
M
DP
=
5
4
Equation of PC is
y
−
1
=
5
4
(
x
−
1
)
. . . (1)
M
AP
=
2
−
2
=
−
1
⇒
M
BC
=
+
1
Equation of
B
C
is
y
−
3
=
(
x
+
2
)
. . . (2)
On solving (1) and (2)
x
+
4
=
5
4
(
x
−
1
)
⇒
4
x
+
16
=
5
x
−
5
⇒
α
=
21
⇒
β
=
y
=
x
+
5
=
26
α
+
β
=
47
Equation of
⟂
bisector of AP
y
−
0
=
(
x
−
2
)
. . . (3)
Equation of
⟂
bisector of
AB
y
−
1
=
5
4
(
x
−
1
2
)
. . . (4)
On solving (3) & (4)
(
x
−
3
)
4
=
5
x
−
5
2
x
=
−
19
2
=
h
y
=
−
23
2
=
k
⇒
2
(
h
+
k
)
=
−
42
© examsnet.com
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