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AP EAPCET 24-Aug-2021 Shift 1 Paper
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© examsnet.com
Question : 42
Total: 160
The equations of sides
A
B
,
B
C
and
C
A
of a triangle
A
B
C
are
2
x
+
y
=
0
,
x
+
p
y
=
q
and
x
−
y
=
3
respectively. If
P
(
2
,
3
)
is its orthocenter, then the value of
p
+
q
equals ______
50
47
65
74
Validate
Solution:
In
Δ
ABC
Equation of AB, BC and CA are
2
x
+
y
=
0
,
x
+
P
y
=
q
and
x
−
y
=
3
respectively.
and
P
(
2
,
3
)
is orthocentre.
Solving
2
x
+
y
=
0
and
x
−
y
=
3
y
=
−
2
x
and
x
+
2
x
=
3
⇒
3
x
=
3
⇒
x
=
1
,
y
=
−
2
∴
A
(
1
,
−
2
)
Slope of
AP
=
3
−
(
−
2
)
2
−
1
=
5
Slope of
BC
=
−
1
p
AP
⊥
BC
⇒
5
×
(
−
1
p
)
=
−
1
p = 5
Now for vertex B
2
x
+
y
=
0
,
y
=
−
2
x
x
+
5
y
=
9
x
−
10
x
=
q
⇒
x
=
−
9
9
,
y
=
21
9
B is
(
−
q
9
,
2
q
9
)
Slope of
BP
=
2
q
9
−
3
−
q
9
−
2
=
2
q
−
27
−
q
−
18
Slope of
AC
=
1
BP
⊥
AC
⇒
(
q
−
27
−
q
−
18
)
(
l
)
=
−
1
⇒
2
q
−
27
=
q
+
18
2
q
−
q
=
18
+
27
q
=
45
p
+
q
=
5
+
45
=
50
© examsnet.com
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