Graphs of Circles Worksheets

How to Find the Equation of a Circle Based on the Diameter and the Center Point - A circle is a set of all points in a plane at a defined distance known as the radius and for the given point called the center. Apart from the radius and center, a circle includes various parts in its geometry. A line segment connecting the two points on the circle and passes through the center of the circle is known as the diameter of the circle. Let's assume that point (x, y) are the coordinates given on the circle. The center of the circle will be at (h, k), and the radius will be defined as the 'r'. Using the distance formula to find the equation of the circle. √(x2 - x1)2 + (y2 – y1)2 = d Substituting (x1 , y1) = (h, k) and (x2 , y2) = (x, y) and d = r √( x – h)2 + (y – k)2 = r Squaring each side (x – h)2 + (y – k )2= r2 The equation of the circle with radius r units and the center (h, k) is (x – h)2 + (y – k )2 = r2.

The Lottery

A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: "1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that...