Dr Md Ataur Rahman Guest Faculty Department of Mathematics ML Arya College Kasba PURNEA UNIVERSITY PURNIA Radical axis Define radical axis and find the equation of the radical axis of two given circles ID: 1038855
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1. Radical axisLecture-12 UG (B.Sc., Part-1) Dr. Md. Ataur RahmanGuest FacultyDepartment of MathematicsM.L. Arya, College, KasbaPURNEA UNIVERSITY, PURNIA
2. Radical axisDefine radical axis and find the equation of the radical axis of two given circles.Definition: The radical axis of two circles is the locus of a point which moves in a plane such that the length of the tangents drawn from it to the circles are equal. P(x,y) i.e. PQ=PR BAQR
3. Equation of Radical axisLet the equations of two circles beLet P(h, k) be any moving point in the plane, then by the definition of radical axis,
4. Equation of Radical axisTherefore the locus of the point P(h, k) iswhich is the required equation of the radical axis.i.e. the equation of the radical axis of two circlesWhere
5. Condition of perpendicularity2. Show that the radical axis of two circles is perpendicular to line of centres (line segment joining the centres of these circles.Solution:- Let the equations of two circles beCentre of circle (1) is Centre of circle (2) is Slope of
6. Condition of perpendicularityThe equation of the radical axis AB isThe slope of the radicalaxisNow, P A BQRadical axis
7. ProblemsFind the equation of the radical axis and the length of the common chord of two circlesFind the equation of the circle whose diameter is the common chord of the circlesFind the equation of the circle whose diameter is the common chord of the circles