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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 60
Total: 100
If the extremities of the base of an isosceles triangle are the points
(
2
a
,
0
)
and
(
0
,
a
)
and the equation of one of the sides is
x
=
2
a
,
then the area of the triangle, in square units, is:
[Online April 23, 2013]
5
4
a
2
5
2
a
2
25
a
2
4
5
a
2
Validate
Solution:
Let
y
-coordinate of
C
=
b
∴
C
=
(
2
a
,
b
)
A
B
=
√
4
a
2
+
a
2
=
√
5
a
Now,
A
C
=
B
C
⇒
b
=
√
4
a
2
+
(
b
−
a
)
2
⇒
b
2
=
4
a
2
+
b
2
+
a
2
−
2
a
b
⇒
2
a
b
=
5
a
2
⇒
b
=
5
a
2
∴
C
=
(
2
a
,
5
a
2
)
Hence area of the triangle
=
1
2
|
2
a
0
1
0
a
1
2
a
5
a
2
1
|
=
1
2
|
2
a
0
1
0
a
1
0
5
a
2
0
|
=
1
2
×
2
a
(
−
5
a
2
)
=
−
5
a
2
2
Since area is always +ve, hence area
=
5
a
2
2
s
q
⋅
u
n
i
t
© examsnet.com
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