Notes 102: Circles

Substituting this into equation (1), we have a2 + 4 5a 3 2 = 4 a2 + (4 5a)2 9 = 4 9a2 +(4 25a) = 36 34a2 40a 20 = 0 from which we ﬁnd a = 40 p 402 4(34)( 20) 68 so a = 0:3783339250 or a = 1:5548045132 Notice that, although mentally we were thinking that we were solving for one of the points of

Equation of a Tangent to a Circle LESSON

Equation of tangent is In general: The equation of the tangent to the circle at the point is You would not get full marks though for simply writing down the answer without showing your working Video: Equation of a tangent to a circle Solutions to Starter and E g s Exercise 9-1 class textbook: p407 E12 10 Qu 1-5, 7, 8, 9*

The equation of a tangent to a circle

The equation of a tangent to a circle Revise to work out the equation of a circle Examples to try 1 Example where you are given the centre and the radius Find the general equation a circle centre (-1;3) with a radius of 5 units 2 Example where you are given the Diameter Determine the equation the circle, given the diameter AB Tangents

Equation of Circles and Tangents - Naiker Maths

www naikermaths com 2 Here is a circle, centre O, and the tangent to the circle at the point P(4, 3) on the circle Find an equation of the tangent at the point P

Equations of the Common Tangents to Two Circles

polar equation: ( 1 + 1 + 2 1+ )+ 2 ( 1+ )+????=0 T x 1, y 1 Polar g1 A g2 B and P 1 Determine the polar equation 2 Substitute to the circle equation to find point A and point B coordinate 3 Use the equation tangent pass trough a point on the circle The equation is same as the polar equation

Exercices sur les équations de cercles Exercice 1

Ecrire l’équation de la tangente en B à ce cercle La tangente à un cercle en un point est une droite perpendiculaire au rayon passant par ce point 15 IA 20 soit 4 IA 2 et 10 OA 20 soit 1 OA 2 Produit scalaire : IA OA 4 1 2 2 4 4 0 u u Donc IA OAA et le cercle C est tangent à Equation de la tangente au cercle en B : le vecteur IA

LE CERCLE

Une droite ( ) est dite tangente à un cercle (????) s’ils se oupent en un seul point Propriété : Une droite ( ) est dite tangente au cercle ????(Ω,????))si et seulement si (Ω,( )= 2 2 Equation de la tangente à un cercle en un de ses points Soit ????(Ω,????) un cercle dans le plan où Ω( , ) et l’un de ses points