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Byju's Answer
Standard XII
Mathematics
Tangent To a Parabola
Find the equa...
Question
Find the equations of tangent and normal to the parabola
y
2
=
4
a
x
at the point
(
a
t
2
,
2
a
t
)
.
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Solution
The equation of the given curve is
y
2
=
4
a
x
.
Differentiating w.r.t. x, we get,
2
y
d
y
d
x
=
4
a
d
y
d
x
=
2
a
y
Slope of tangent to the curve at
(
a
t
2
,
2
a
t
)
=
2
a
2
a
t
=
1
t
Therefore, equation of the tangent is
(
y
−
2
a
t
)
=
1
t
(
x
−
a
t
2
)
y
t
−
2
a
t
2
=
x
−
a
t
2
x
−
t
y
+
a
t
2
=
0
Slope of normal to the curve at
(
a
t
2
,
2
a
t
)
is
−
t
.
Therefore, equation of the normal is
(
y
−
2
a
t
)
=
−
t
(
x
−
a
t
2
)
x
t
+
y
−
2
a
t
−
a
t
2
=
0
x
t
+
y
−
a
t
(
2
+
t
)
=
0
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Similar questions
Q.
Find the equations of the tangent and normal to the parabola
y
2
= 4
ax
at the point (
at
2
, 2
at
).