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AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 57
Total: 160
A straight line passing through
A
(
3
,
1
)
meets the coordinate axes at
P
and
Q
such that its distance from the origin
O
is maximum. Then area of
∆
O
P
Q
is ______sq.units
100
3
25
3
50
3
200
3
Validate
Solution:
A
=
(
3
,
1
)
Let slope of line be
m
∴
y
−
y
1
=
m
(
x
−
x
1
)
[be the required line]
y
−
1
=
m
(
x
−
3
)
y
−
1
=
m
x
−
3
m
m
x
−
y
+
(
1
−
3
m
)
=
0
....(i)
The greatest distance of line from origin passes through
A
(
3
,
1
)
is perpendicular to the given line.
∴
O
A
⟂
P
Q
Slope of
O
A
×
Slope of
P
Q
=
−
1
1
3
×
m
=
−
1
⇒
m
=
−
3
Put,
m
=
−
3
in Eq. (i)
−
3
x
−
y
+
(
1
−
3
)
(
−
3
)
=
0
−
3
x
−
y
+
(
10
)
=
0
3
x
+
y
+
10
=
0
∴
Area of
∆
P
O
Q
=
1
2
|
c
2
a
b
|
=
1
2
|
100
3
×
1
|
=
50
3
s
q
units
© examsnet.com
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