Length Of Tangent, Sub Tangent, Normal, Examples, Important Topics For JEE 2024 | PW
Shrivastav 20 Mar, 2024
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Length Of Tangent : Tangent to any curve is defined as limiting case of secant it means tangent either touches the curve or not such as shown below
at point
c
Length of Tangent
Length of tangent is defined as the portion of the tangent between curve and x axis such as
Length of Subtangent
Length of subtangent is defined as the shadow of the length of tangent on x axis such as
Length of Normal
Length of Normal is defined as intercept of normal with the curve and x axis such as
Length of Subnormal
Length of Subnormal is defined as shadow of the length of normal on x axis such as
Length Of Tangent Introduction
Length of tangent, Normal, Subtangent, Subnormal can be derived using differential method let’s find it
In above graph we have a curve
{using identity
}
Length of tangent of the curve would be
AB
where
x
ε
A
Coordinate
where
x
ε
A
Coordinate
Length of subtangent of the curve would be
BD
where
x
ε
A
Coordinate
Length of Normal of the curve would be
AC
In Δ
ACD
{using identity
}
where
x
ε
A
Coordinate
where
x
ε
A
Coordinate
Length of subnormal of the curve would be
CD
where
x
ε
A
Coordinate
Examples Based On Length Of Tangent, Normal To The Curve
Example 1:
Find length of tangent to parabola
Sol. Given point satisfies the curve hence it’s a point of contact Now length of tangent at any random point of contact is
Now
at (4, 8) is 1
Length of tangent would be
Example 2:
Find length of Normal to Ellipse
Sol. Given point satisfies the curve hence it’s a point of contact Now length of Normal at any random point of contact is
Now
at (2, 0) is undefined means angle of tangent must be
Length of normal would be undefined.
Rapid Questions Based On Length Of Tangent
1.
Find length of tangent to parabola
2.
A tangent is drawn to the curve
Illustrations based on length of tangent
1.
A tangent drawn to the curve
Sol.
Equation of tangent to the curve from the point (6, 0) would be as
we have
we have
length of tangent
=
=0
length of normal=
= 0
length of subtangent =
length of subnormal =
Rapid Questions Based On Length Of Tangent
1.
A tangent drawn to the curve
2.
Find length of tangent, subtangent, normal and subnormal to parabola
Length of Tangent FAQs
Q.1: What is tangent on a curve?
Q.2 : What is normal on a curve?
Q.3 : How length of subtangent is different from length of subnormal?
Q.4 : What does derivative of any function represent?
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