A fascinating fact about the motions of all heavenly bodies (planets, comets, etc.) is that they all move in conic sections. Conic sections are the ellipse, parabola, hyperbola, and the circle . In fact all objects under the influence of gravity moves in conic sections. Conic sections can be written in mathematics and they are as follows : Circles. A circle is the set of points in a plane whose distance from a given fixed point in the plane is constant. The fixed point is the center of the circle ; the constant distant is the radius . The equation of a circle of radius centered at the point is : (a is the radius of the circle.) Parabolas. A set that consists of all the points in a plane equidistant from a given fixed point and a given fixed line in the plane is a parabola . The fixed point is the focus of the parabola. The fixed line is the directrix . It's standard form is : (p is the parabola's focal length.) Ellipses. An ellipse is the set of points in a plane whose distances from two fixed points in a plane have a constant sum. The two fixed points are the foci of the ellipse. It's standard form is : (a is the semimajor axis and b is the simiminor axis of the ellipse.) Hyperbolas. A hyperbola is the set of points in a plane whose distances from two fixed points in the plane have a constant difference. The two fixed points are the foci of the hyperbola. It's standard form is :