Tools to use Calculus
Circles and Parabolas		Shifty Business
A Circle is a set of points in a plane whose distance from a fixed point in the plane is constant. Since we have a Cartesian Plane we know that distance is defined by the metric . Call fixed point (h, k) the center of the circle having a radius a and we can write the Standard Equation of a Circle. (x - h)2 + (y - k)2 = a2 If the center is at the Origin the equation reduces to the Pythagorean Theorem. The slides over on the right side of this page illustrate the utility of the Standard Equation of a Circle. Parabolas are everywhere. Knock something off a table and its path is parabolic as it approaches the floor. Throw a ball to someone and its course describes a parabola through the air. Headlights and reflecting telescopes use parabolic mirrors; one to send out a straight beam of light and the other to focus incoming light into a single point. The equation and graph of a parabola has numerous elements which serves to confuse the simplicity of what a parabola is. Apply some Style and this confusion can be clarified.
The curve is a parabola with its Focus at (0, 1). The line segment PD is always perpendicular to the line y = -p, which in this case is y = -1. As long as the point P is a point on the curve the line segments PD equals the line segment PF.
Trigonometry - section five		Tools to use Calculus - section topics