Tangent AND Normal formulas

Every formula JEE Advanced expects you to know for Tangent AND Normal, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 129 practice questions

Formulas: 34
Subject: Mathematics
Exam: JEE Advanced
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Tangent AND Normal, every formula

34 formulas, typeset and free. Print it, or keep it open beside your practice.

Slope of tangent
$m = tan θ = \frac{d y}{d x}_{(x_{1}, y_{1})}$
Slope for f(x,y)=0
$m = - (\frac{\partial f / \partial x}{\partial f / \partial y})_{(x_{1}, y_{1})}$
Slope (parametric)
$m = \frac{g ^{'} ( t )}{f ^{'} ( t )}$
x=f(t), y=g(t)
Tangent parallel to x-axis
$\frac{d y}{d x} = 0$
Tangent perpendicular to x-axis
$\frac{d y}{d x} \to \infty or \frac{d x}{d y} = 0$
Equation of tangent
$y - y_{1} = m (x - x_{1})$
Equation of normal
$y - y_{1} = - \frac{1}{m} (x - x_{1})$
Slope of normal
$- \frac{1}{d y / d x}$
Tangent at origin (lowest degree)
$equate lowest-degree terms to 0$
Equally inclined tangent
$\frac{d y}{d x} = \pm 1$
Length of tangent
$P T = \frac{y _{1} 1 + m ^{2}}{m}$
Length of normal
$P N = y_{1} 1 + m^{2}$
Length of sub-tangent
$T M = \frac{y _{1}}{m}$
Length of sub-normal
$M N = ∣ y_{1} m ∣$
Sub-tangent/normal in GP
$y_{1}^{2} = (sub-tangent) (sub-normal)$
Angle between two curves
$tan θ = \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}}$
Curves touch
$m_{1} = m_{2}$
Orthogonal curves
$m_{1} m_{2} = - 1$
Orthogonal (implicit)
$\frac{\partial f}{\partial x} \frac{\partial g}{\partial x} + \frac{\partial f}{\partial y} \frac{\partial g}{\partial y} = 0$
Rate of change
$\frac{d y}{d t} = \frac{d y}{d x} \cdot \frac{d x}{d t}$
Velocity
$v = \frac{d s}{d t}$
Acceleration
$a = \frac{d v}{d t} = \frac{d ^{2} s}{d t ^{2}} = v \frac{d v}{d s}$
Differential (approximation)
$d y = f^{'} (x) δ x$
Approx value
$f (x + δ x) \approx f (x) + f^{'} (x) δ x$
Relative error
$\frac{δ y}{y}$
Percentage error
$\frac{δ y}{y} \times 100$
Error in kxⁿ
$\frac{δ y}{y} = n \frac{δ x}{x}$
f=kxⁿ
Area of triangle (xy=c²)
$2 c^{2} sq. units$
tangent + axes
Sphere surface & volume
$S = 4 π r^{2}, V = \frac{4}{3} π r^{3}$
Cylinder surface & volume
$S = 2 π r h + 2 π r^{2}, V = π r^{2} h$
Cone: l, curved & total surface
$l^{2} = r^{2} + h^{2}, CSA = π r l, TSA = π r^{2} + π r l$
Cone volume
$V = \frac{1}{3} π r^{2} h$
Sector arc, area
$l = r θ, A = \frac{1}{2} r^{2} θ$
Simple pendulum period
$T = 2 π \frac{l}{g}$

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Tangent AND Normal formulas

Tangent AND Normal, every formula

Slope of tangent

Slope for f(x,y)=0

Slope (parametric)

Tangent parallel to x-axis

Tangent perpendicular to x-axis

Equation of tangent

Equation of normal

Slope of normal

Tangent at origin (lowest degree)

Equally inclined tangent

Length of tangent

Length of normal

Length of sub-tangent

Length of sub-normal

Sub-tangent/normal in GP

Angle between two curves

Curves touch

Orthogonal curves

Orthogonal (implicit)

Rate of change

Velocity

Acceleration

Differential (approximation)

Approx value

Relative error

Percentage error

Error in kxⁿ

Area of triangle (xy=c²)

Sphere surface & volume

Cylinder surface & volume

Cone: l, curved & total surface

Cone volume

Sector arc, area

Simple pendulum period

More JEE Advanced Mathematics formula sheets

Know the Tangent AND Normal formulas. Now use them.

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