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  2. Radical axis - Wikipedia

    en.wikipedia.org/wiki/Radical_axis

    If the radii are equal, the radical axis is the line segment bisector of M 1, M 2. In any case the radical axis is a line perpendicular to ¯. On notations. The notation radical axis was used by the French mathematician M. Chasles as axe radical. [1] J.V. Poncelet used chorde ideale. [2]

  3. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    Firstly, if a < 0, the change of variable x → –x allows supposing a > 0. After this change of variable, the new graph is the mirror image of the previous one, with respect of the y-axis. Then, the change of variable x = x 1 – ⁠ b / 3a ⁠ provides a function of the form = + +.

  4. Power center (geometry) - Wikipedia

    en.wikipedia.org/wiki/Power_center_(geometry)

    The three radical axes meet in a single point, the radical center, for the following reason. The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal: h 1 = h 2.

  5. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    For solving the cubic equation x 3 + m 2 x = n where n > 0, Omar Khayyám constructed the parabola y = x 2 /m, the circle that has as a diameter the line segment [0, n/m 2] on the positive x-axis, and a vertical line through the point where the circle and the parabola intersect above the x-axis.

  6. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Construction of the Malfatti circles: [3] For a given triangle determine three circles, which touch each other and two sides of the triangle each. Spherical version of Malfatti's problem: [4] The triangle is a spherical one. Essential tools for investigations on circles are the radical axis of two circles and the radical center of three circles.

  7. Power diagram - Wikipedia

    en.wikipedia.org/wiki/Power_diagram

    The radical axis of two intersecting circles. The power diagram of the two circles is the partition of the plane into two halfplanes formed by this line. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along the radical axis, both circles have equal power.

  8. Problem of Apollonius - Wikipedia

    en.wikipedia.org/wiki/Problem_of_Apollonius

    In summary, the desired line L 1 is defined by two points: the radical center G of the three given circles and the pole in C 1 of one of the four lines connecting the homothetic centers. Finding the same pole in C 2 and C 3 gives L 2 and L 3, respectively; thus, all six points can be located, from which one pair of solution circles can be found ...

  9. Matrix representation of conic sections - Wikipedia

    en.wikipedia.org/wiki/Matrix_representation_of...

    In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections.It provides easy ways to calculate a conic section's axis, vertices, tangents and the pole and polar relationship between points and lines of the plane determined by the conic.