MATH 103 Lecture Notes - Lecture 12: Parametric Equation, Apollonian Circles, Radical Axis

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Circle is defined as the locus of a point which moves in a plane such that its distance from a fixed point in that plane is constant. Standard forms of a circle (i) equation of circle having centre (h, k) and radius (x h)2 + (y k)2 = a2. The general equation of a circle is given by x2 + y2 + 2gx + 2fy + c = 0, where centre of the circle = (- g, f) Radius of the circle = g2 + f2 c: if g2 + f2 c > 0, then the radius of the circle is real and hence the circle is also real. If g2 + f2 c = 0, then the radius of the circle is 0 and the circle is known as point circle. If g2 + f2 c< 0, then the radius of the circle is imaginary. Such a circle is imaginary, which is not possible to draw.

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