1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Equation of Tangent at a Point (x,y) in Terms of f'(x)
Find the equa...
Question
Find the equation of the tangent and the normal to the following curve at the indicated point.
y
2
=
4
a
x
at
(
x
1
,
y
1
)
.
Open in App
Solution
y
2
=
4
a
x
Differentiating both sides w.r.t.
x
,
⇒
2
y
d
y
d
x
=
4
a
⇒
d
y
d
x
=
2
a
y
Slope of tangent at
(
x
1
,
y
1
)
=
(
d
y
d
x
)
(
x
1
,
y
2
)
=
2
a
y
1
=
m
Equation of tangent is,
y
−
y
1
=
m
(
x
−
x
1
)
⇒
y
−
y
1
=
2
a
(
x
−
x
1
)
y
1
⇒
y
y
1
−
y
2
1
=
2
a
x
−
2
a
x
1
⇒
y
y
1
−
4
a
x
1
=
2
a
x
−
2
a
x
1
⇒
y
y
1
=
2
a
x
+
2
a
x
1
⇒
y
y
1
=
2
a
(
x
+
x
1
)
Equation of normal is,
y
−
y
1
=
1
S
l
o
p
e
o
f
t
a
n
g
e
n
t
(
x
−
x
1
)
⇒
y
−
y
1
=
−
1
m
(
x
−
x
1
)
⇒
y
−
y
1
=
−
y
1
2
a
(
x
−
x
1
)
∴
Equation of tangent is
y
y
1
=
2
a
(
x
+
x
1
)
∴
Equation of normal is
y
−
y
1
=
−
y
1
2
a
(
x
−
x
1
)
Suggest Corrections
0
Similar questions
Q.
Find the equations of the tangent and the normal, to the curve
16
x
2
+
y
2
=
145
at the point
(
x
1
,
y
1
)
, where
x
1
=
2
and
y
1
>
0
.
Q.
The equation of the tangent at
(
x
1
,
y
1
)
to a curve
y
2
=
4
a
x
at a point
(
x
1
,
y
1
)
is given by
y
y
1
=
2
a
(
x
+
x
1
)
Q.
The equation of the tangent at
(
x
1
,
y
1
)
to a curve
y
2
=
4
a
x
at a point
(
x
1
,
y
1
)
is given by
y
y
1
=
2
a
(
x
+
x
1
)
Q.
Find the equation of the tangent and the normal to the following curve at the indicated point.
x
=
a
sec
t
,
y
=
b
tan
t
at
t
.
Q.
Find the equation of the tangent and the normal to the following curve at the indicated point.
y
=
2
x
2
−
3
x
−
1
at
(
1
,
−
2
)
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Explore more
Equation of Tangent at a Point (x,y) in Terms of f'(x)
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app