HP Prime Graphing NW280AAABA manual Pole, Powerpc, Radicalaxis, Reciprocation

pole

Returns the pole of the given line with respect to the given circle.

pole(circle, line)

Example:

pole(circle(x^2+y^2=1), line(x=3)) returns point(1/3, 0)

powerpc

Given a circle and a point, returns the difference between the square of the distance from the point to the circle’’s center and the square of the circle’s radius.

powerpc(circle, point)

Example

powerpc(circle(point(0,0), point(1,1)- point(0,0)), point(3,1)) returns 8

radical_axis

Returns the line whose points all have the same powerpc values for the two given circles.

radical_axis(circle1, circle2)

Example:

radical_axis(circle(((x+2)²+y²) = 8),circle(((x-2)²+y²) = 8)) returns line(x=0)

reciprocation

Given a circle, returns the poles (points) of given polar lines or the polar lines of given poles (points).

reciprocation(circle, point) or reciprocation(circle, line) or reciprocation(circle, list)

Example:

reciprocation(circle(x^2+y^2=1),{point(1/ 3,0), line(x=2)}) returns [line(x=3), point(1/ 2, 0)]

192 Geometry