Hyperbola formulas

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

Practise these formulas 197 practice questions

Formulas: 36
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Hyperbola, every formula

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

Standard equation
$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$
Eccentricity
$e = \frac{a ^{2} + b ^{2}}{a}, b^{2} = a^{2} (e^{2} - 1)$
Eccentricity condition
$e > 1$
Foci
$(\pm a e, 0)$
Vertices
$(\pm a, 0)$
Length of latus rectum
$\frac{2 b ^{2}}{a}$
Transverse & conjugate axes
$2 a (transverse), 2 b (conjugate)$
Directrices
$x = \pm \frac{a}{e}$
Ends of latus rectum
$(\pm a e, \pm \frac{b ^{2}}{a})$
Focal distance difference
$∣ S P - S^{'} P ∣ = 2 a$
Conjugate hyperbola
$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = - 1$
Eccentricities relation
$\frac{1}{e _{1}^{2}} + \frac{1}{e _{2}^{2}} = 1$
Parametric equations
$x = a sec θ, y = b tan θ$
Auxiliary circle
$x^{2} + y^{2} = a^{2}$
Director circle
$x^{2} + y^{2} = a^{2} - b^{2}$
Rectangular hyperbola
$a = b \Rightarrow e = 2$
Notation S₁₁
$S_{11} = \frac{x _{1}^{2}}{a ^{2}} - \frac{y _{1}^{2}}{b ^{2}} - 1$
Position of a point
$S_{11} < 0 outside, = 0 on, > 0 inside$
Tangent at (x₁,y₁)
$\frac{x x _{1}}{a ^{2}} - \frac{y y _{1}}{b ^{2}} = 1$
Tangent at θ
$\frac{x}{a} sec θ - \frac{y}{b} tan θ = 1$
Tangent of slope m
$y = m x \pm a^{2} m^{2} - b^{2}$
Tangency condition
$c^{2} = a^{2} m^{2} - b^{2}$
for y=mx+c
Normal at (x₁,y₁)
$\frac{a ^{2} x}{x _{1}} + \frac{b ^{2} y}{y _{1}} = a^{2} + b^{2}$
Normal of slope m
$y = m x \mp \frac{m ( a ^{2} + b ^{2} )}{a ^{2} - b ^{2} m ^{2}}$
Asymptotes
$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 0 \Rightarrow y = \pm \frac{b}{a} x$
Angle between asymptotes
$2 tan^{- 1} \frac{b}{a}$
Hyperbola - asymptote constant
$hyperbola and its asymptote pair differ by a constant$
S + S' = 2A
$hyperbola + conjugate = 2 \times asymptote pair$
Rectangular hyperbola xy=c²
$x y = c^{2}, c^{2} = \frac{a ^{2}}{2}$
xy=c² parametric
$x = c t, y = \frac{c}{t}$
xy=c² tangent at t
$x + y t^{2} = 2 c t$
xy=c² normal at t
$x t^{3} - y t = c (t^{4} - 1)$
Chord of contact
$\frac{x x _{1}}{a ^{2}} - \frac{y y _{1}}{b ^{2}} = 1 (S_{1} = 0)$
Product of ⊥ from foci to tangent
$b^{2}$
Reflection property
$ray toward one focus reflects toward the other focus$
Co-normal points sum
$α + β + γ + δ = odd multiple of π$
eccentric angles

Know the Hyperbola formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Hyperbola formulas

Hyperbola, every formula

Standard equation

Eccentricity

Eccentricity condition

Foci

Vertices

Length of latus rectum

Transverse & conjugate axes

Directrices

Ends of latus rectum

Focal distance difference

Conjugate hyperbola

Eccentricities relation

Parametric equations

Auxiliary circle

Director circle

Rectangular hyperbola

Notation S₁₁

Position of a point

Tangent at (x₁,y₁)

Tangent at θ

Tangent of slope m

Tangency condition

Normal at (x₁,y₁)

Normal of slope m

Asymptotes

Angle between asymptotes

Hyperbola - asymptote constant

S + S' = 2A

Rectangular hyperbola xy=c²

xy=c² parametric

xy=c² tangent at t

xy=c² normal at t

Chord of contact

Product of ⊥ from foci to tangent

Reflection property

Co-normal points sum

More JEE Advanced Mathematics formula sheets

Know the Hyperbola formulas. Now use them.

Join QuestPix, Today!