Polar of a point with respect to a circle: If 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 (T) 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 of point and pole is a point with respect to which polar is determined.
Equation to the polar of the point (x1,y1) w.r.t. to the circle x² + y² = a² is
xx1+yy1 = a²
The polar of the point (x1,y1) w.r.t. to the circle x² + y²+2gx+2fy+c = 0 is given by
(xx1 + yy1 +g(x+x1)+f(y+y1) +c) = 0
The equation is same as the equation for the tangent to the circle at a point (x1,y1) on the circle.
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