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Byju's Answer
Standard XII
Mathematics
Tangent of a Curve y =f(x)
At what point...
Question
At what point the slope of the tangent to the curve x
2
+ y
2
− 2x − 3 = 0 is zero
(a) (3, 0), (−1, 0)
(b) (3, 0), (1, 2)
(c) (−1, 0), (1, 2)
(d) (1, 2), (1, −2)
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Solution
(d) (1, 2), (1, −2)
Let (x
1
, y
1
) be the required point.
Since
,
the
point
lie
on
the
curve
.
Hence
,
x
1
2
+
y
1
2
-
2
x
1
-
3
=
0
.
.
.
1
Now
,
x
2
+
y
2
-
2
x
-
3
=
0
⇒
2
x
+
2
y
d
y
d
x
-
2
=
0
∴
d
y
d
x
=
2
-
2
x
2
y
=
1
-
x
y
Now
,
Slope of the tangent =
d
y
d
x
x
1
,
y
1
=
1
-
x
1
y
1
S
lope of the tangent=0 (Given)
∴
1
-
x
1
y
1
=
0
⇒
1
-
x
1
=
0
⇒
x
1
=
1
From (1), we get
x
1
2
+
y
1
2
-
2
x
1
-
3
=
0
⇒
1
+
y
1
2
-
2
-
3
=
0
⇒
y
1
2
-
4
=
0
⇒
y
1
=
±
2
So, the points are
1
,
2
and
1
,
-
2
.
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