Home
Learn
Plan & Focus
Community
Pricing
Play & Compete
Free Resources

Log in Join Free

by JEE Master

Ask. Share. Learn. Grow Together. India's all-in-one community for JEE Main & JEE Advanced aspirants.

Explore

Learn
Plan & Focus
Community
Play & Compete
Free Resources

Resources

JEE Main PYQs
JEE Advanced PYQs
Formula Sheets
NCERT Mapping
Mock Analysis

Support

Help Center
Privacy Policy
Terms of Use
Contact Us

© 2026 PadhoNa. All rights reserved.

Formula Sheets / Maths

Chapter 24

Circle

Revise with flashcards Download this chapter (PDF) All Maths formulas (PDF)

Equations Point, line and power Tangent, normal and chord Two circles

Equations

Centre–radius
$(x - h)^{2} + (y - k)^{2} = r^{2}$
General
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0 :$ centre $(- g, - f), r = g^{2} + f^{2} - c$
Diameter form
$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$
Parametric
$x = h + r cos θ, y = k + r sin θ$

Point, line and power

Power of a point
$S_{1} = x_{1}^{2} + y_{1}^{2} + 2 g x_{1} + 2 f y_{1} + c : S_{1} < 0$ inside $, = 0$ on $, > 0$ outside
Line and circle
perpendicular distance from centre $<, =, > r :$ secant, tangent, misses
Tangent condition
$y = m x + c$ touches $x^{2} + y^{2} = a^{2} ⟺ c^{2} = a^{2} (1 + m^{2})$

Tangent, normal and chord

Tangent at a point
$T = 0 : x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c = 0$
Length of tangent
$S_{1}$
Chord with given midpoint
$T = S_{1}$
Chord of contact
$T = 0$ (from an outside point)
Pair of tangents
$S S_{1} = T^{2}$
Normal
always passes through the centre

Two circles

Common tangents
$d > r_{1} + r_{2} : 4; d = r_{1} + r_{2} : 3; ∣ r_{1} - r_{2} ∣ < d < r_{1} + r_{2} : 2; d = ∣ r_{1} - r_{2} ∣ : 1; d < ∣ r_{1} - r_{2} ∣ : 0$
Orthogonal circles
$2 g_{1} g_{2} + 2 f_{1} f_{2} = c_{1} + c_{2}$
Radical axis / common chord
$S_{1} - S_{2} = 0$
Family
$S + λ L = 0,$ $S_{1} + λ S_{2} = 0$

Straight Lines Parabola