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Byju's Answer
Standard XII
Mathematics
Conic Section
The point on ...
Question
The point on the curve
y
=
x
2
+
4
at which the tangent is perpendicular to the line
x
+
2
y
=
3
is
A
(
−
1
,
5
)
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B
(
5
,
1
)
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C
(
1
,
5
)
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D
(
1
,
−
5
)
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Solution
The correct option is
D
(
1
,
5
)
Given,
y
=
x
2
+
4
d
y
d
x
=
2
x
let the points on the curve be,
α
,
β
d
y
d
x
α
,
β
=
2
α
=
m
1
x
+
2
y
=
3
slope of the above line,
m
2
=
−
1
2
we have,
m
1
m
2
=
−
1
m
1
(
−
1
2
)
−
1
m
1
=
2
⇒
2
α
=
2
∴
α
=
1
⇒
β
=
(
1
)
2
+
4
=
5
Therefore the point is
(
1
,
5
)
Suggest Corrections
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