Circle - Definitions- July - Dec Revision

Some definitions

A circle is defined as the locus of a point which moves in a plane such that its distance form a fixed point in that plane is always fixed.

Intercept of the circle on x axis is the length of chord of the circle which is a part of x axis.

Similarly Intercept of the circle on y axis is the length of chord of the circle which is a part of y axis.

Director circle: the locus of the point of intersection of two perpendicular tangents to a given conic is known as its director circle.

Chord of contact: the chord joining the points of contact of the two tangents to a conic drawn from a given point, outside it, is called the chord of contact of tangents.

Pole and Polar:
Polar of a point with respect to a circle: Of through a point P(x1,y1) (inside or outside a circle) there be drawn any straight line to meet the given circle a Q and R, the locus of the point of intersection of the tangents at Q and R is called the polar of point P and P is the called the pole of the polar.

Polar is the locus and pole is a point.

Diameter – definition as a locus: the locus of the middle points of a system of parallel chords of a circle is called a diameter of the circle.

Common chord of two circles: The chord joining the points of intersection of two given circles is called their common chord.

Angle of intersection of two curves: If the two curves C1 and C2 intersect at a point P and PT1 and PT2 be the tangents to the two curves C1 and C2 respectively at P. Then the angle between the tangents at P is called the angle of intersection of the two curves at the point of intersection.

Orthogonal curves: Two curves are said to intersect orthogonally when the two tangents at the common point are at right angles.

Radical axis: the radical axis of two circles is the locus of a point which moves in such a way that the lengths of the tangents drawn from it to the two circles are equal.

Radical centre: The point of concurrence of the radical axes of three circles whose centres are non-collinear, taken in pairs, is called the radical centre of the circles.

Coaxial system of circles: A system of circles, every pair of which has the same radical axis is called a coaxial system of circles.

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