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Byju's Answer
Standard XII
Mathematics
Point Form of Normal:Hyperbola
The slope of ...
Question
The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.
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Solution
According to the question,
d
y
d
x
=
1
2
y
⇒
2
y
d
y
=
d
x
Integrating
both
sides
,
we
get
2
∫
y
d
y
=
∫
d
x
⇒
y
2
=
x
+
C
Since
the
curve
passes
throught
the
point
4
,
3
,
it
satisfies
the
equation
of
the
curve
.
9
=
4
+
C
⇒
C
=
5
Putting
the
value
of
C
in
the
equation
of
the
curve
,
we
get
y
2
=
x
+
5
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