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Question
Mathematics
Let y=y(x) be a function of x satisfying y√1-x2=k-x√1-y2 where k is a constant and y((1/2)) =-(1/4). Then (dy/dx) at x=(1/2), is equal to :
Q. Let
y
=
y
(
x
)
be a function of
x
satisfying
y
1
−
x
2
=
k
−
x
1
−
y
2
where
k
is a constant and
y
(
2
1
)
=
−
4
1
.
Then
d
x
d
y
at
x
=
2
1
,
is equal to :
3728
208
JEE Main
JEE Main 2020
Continuity and Differentiability
Report Error
A
−
2
5
61%
B
2
5
16%
C
−
4
5
16%
D
5
2
8%
Solution:
Put
x
=
s
in
θ
,
y
=
s
in
α
y
1
−
x
2
=
k
−
x
1
−
y
2
⇒
s
in
α
⋅
cos
θ
+
cos
α
⋅
s
in
θ
=
k
⇒
s
in
(
α
+
θ
)
=
k
⇒
α
+
θ
=
s
i
n
−
1
k
⇒
s
i
n
−
1
x
+
s
i
n
−
1
y
=
s
i
n
−
1
k
⇒
1
−
x
2
1
+
1
−
y
2
1
×
d
x
d
y
=
0
at
x
=
2
1
,
y
=
4
−
1
d
x
d
y
=
2
−
5