The Quadratic Curve Addition Method. ( QCAM)

My motive for this study is "a circle circumscribing multiple circles" or "a circle circumscribing each other within a circle". Hereinafter I referred to those circles as "a circle circumscribing multiple circles".

When I proceeded with research on drawing methods to overcome this difficulty, I found that the center of the circle was related to the locus of the quadratic curve.

Therefore, I examined the definition of quadratic curves by elementary geometry, deepened our research on drawing, and tried to systematize the "Quadratic Curve Addition Method" as a drawing method in which the locus of a quadratic curve was added to the drawing by a straightedge and compass. Hereafter, the "Quadratic Curve Addition Method" referred to as QCAM.

The feature of this construction method is to find the center of the circle by finding out the mathematical features of the quadratic curve from the given figure and subject.

Parabola

Let a point F and a straight line l be in a plane. The locus of the point P in the plane whose distance from F and l is equal is called a parabola.

The point F is focus and the line l is the directrix of the parabola

Ellipse

The locus of the point P of a plane whose sum of distances from two fixed points F, F' is constant, that is PF + PF' =2a, is called an ellipse. The two fixed points are called the foci or focuses

Hyperbola

Let F and F be fixed points. The locus of the point P whose difference of distances from two fixed points is constant, that is, |PF - PF'| = 2a, is called hyperbola. The two fixed points are called the foci (focuses).