What is "radical axis"

n. (context mathematics English) The line containing the locus of points from which the segments respectively tangent to two given circles have equal length.

The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length. For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles (orthogonally); conversely, the center of any circle that cuts both circles orthogonally must lie on the radical axis. In technical language, each point P on the radical axis has the same power with respect to both circles

R = d − r = d − r

where r and r are the radii of the two circles, d and d are distances from P to the centers of the two circles, and R is the radius of the unique orthogonal circle centered on P.

The radical axis is always a straight line and always perpendicular to the line connecting the centers of the circles, albeit closer to the circumference of the larger circle. If the circles intersect, the radical axis is the line passing through the intersection points; similarly, if the circles are tangent, the radical axis is simply the common tangent. In general, two disjoint, non-concentric circles can be aligned with the circles of bipolar coordinates; in that case, the radical axis is simply the y-axis; every circle on that axis that passes through the two foci intersect the two circles orthogonally. Thus, two radii of such a circle are tangent to both circles, satisfying the definition of the radical axis. The collection of all circles with the same radical axis and with centers on the same line is known as a pencil of coaxal circles.

Radical Axis (also known as radicalaxis or Radical Axis, Inc.) is an animation studio headquartered in Atlanta, Georgia, United States known for its diverse work in both episodic television and commercials. Founded in 2000 by Scott Fry, an original animator on Aqua Teen Hunger Force for Adult Swim, Radical Axis has since become one of the fastest growing studios in the Southeast. In addition to Aqua Teen Hunger Force, the studio's television credits include Squidbillies, Perfect Hair Forever, 12 oz. Mouse, Sealab 2021, Freak Show on Comedy Central, and Archer for FX. Radical Axis also animated the full-length film, Aqua Teen Hunger Force Colon Movie Film For Theaters.