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MHT CET 2017 Math Solved Paper
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© examsnet.com
Question : 29
Total: 50
The point on the curve y =
√
x
−
1
, where the tangent is perpendicular to the line 2x + y - 5 = 0 is
(2,-1)
(10,3)
(2,1)
(5,-2)
Validate
Solution:
(c) Suppose that slope of the curve y
=
√
x
−
1
is
m
1
∴
m
1
=
d
y
d
x
=
d
d
x
√
x
−
1
1
2
√
x
−
1
slope of the line
2
x
+
y
−
5
=
0
is
m
2
∴
m
2
=
d
y
d
x
=
d
d
x
(
5
−
2
x
)
=
−
2
As, lines are perpendicular if
m
1
m
2
=
−
1
So,
1
2
√
x
−
1
⋅
(
−
2
)
=
−
1
⇒
√
x
−
1
=
1
⇒
x
−
1
=
1
⇒
x
=
2
After substituting
x
=
2
in
y
=
√
x
−
1
,
we get
y
=
1
Hence, required point is
(
2
,
1
)
.
© examsnet.com
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