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Byju's Answer
Standard XII
Mathematics
Tangent of a Curve y =f(x)
At what point...
Question
At what points on the curve y = x
2
− 4x + 5 is the tangent perpendicular to the line 2y + x = 7?
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Solution
Let (x
1
, y
1
) be the required point.
Slope of the given line =
-
1
2
Slope of the line perpendicular to this line = 2
Since
,
the
point
lies
on
the
curve
.
Hence
,
y
1
=
x
1
2
-
4
x
1
+
5
.
.
.
1
Now
,
y
=
x
2
-
4
x
+
5
∴
d
y
d
x
=
2
x
-
4
Now
,
Slope of the tangent at
x
1
,
y
1
=
d
y
d
x
x
1
,
y
1
=2
x
1
-4
Slope of the tangent at
x
1
,
y
1
=Slope of the given line [Given]
∴
2
x
1
-
4
=
2
⇒
2
x
1
=
6
⇒
x
1
=
3
Also
,
y
1
=
9
-
12
+
5
=
2
[
From eq. (1)]
Thus, the required point is
3
,
2
.
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0
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