Radical axis Lecture12 UG B Sc Part1 Dr

Radical axis Lecture-12 UG (B. Sc. , Part-1) Dr. Md. Ataur Rahman Guest Faculty Department of Mathematics M. L. Arya, College, Kasba PURNEA UNIVERSITY, PURNIA

Radical axis 1. Define 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 R Q A B

Equation of Radical axis Let the equations of two circles be Let P(h, k) be any moving point in the plane, then by the definition of radical axis,

Equation of Radical axis Therefore the locus of the point P(h, k) is which is the required equation of the radical axis. i. e. the equation of the radical axis of two circles Where

Condition of perpendicularity 2. 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 be Centre of circle (1) is Centre of circle (2) is Slope of

Condition of perpendicularity The equation of the radical axis AB is The slope of the radical axis Now, A Radical axis P Q B

Problems 1. Find the equation of the radical axis and the length of the common chord of two circles 2. Find the equation of the circle whose diameter is the common chord of the circles 3. Find the equation of the circle whose diameter is the common chord of the circles