Determine whether each point is on the circle. Let’s see how this works by example.Ĭonsider the circle whose equation is ( x - 3) 2 + y 2 = 169. Then sweep out a circle!Įxample - Determining Whether Points Are on a CircleĪ point ( x, y) in the plane is on a circle if and only if that point satisfies the equation of the circle. Place one point of the compass on the center (1, –2), and the drawing point of the compass on a point that is 5 units away, such as (1 + 5, –2) = (6, –2). If you have graph paper and a compass handy, start by drawing and labeling the coordinate axes. Therefore, the circle represented by this equation has center at (1, –2) and radius 5. Now we can read off the values of h, k, and r from the equation. In this case, that’s pretty easy, because we all know that 25 = 5 2. The trick here is to change the plus into the equivalent minus negative.Īlso, you have to make the constant 25 match r 2 from the template. Your job is to make the given equation look exactly like the template. It looks almost the same, except that there is a plus (+) in the second group, instead of a minus (–). To illustrate how the equation of a circle works, let’s graph the circle whose equation is:įirst, compare the given equation with the master template above. Example - Graphing a Circle from its Equation On the other hand, the letters x and y are variables - they do not have a particular value, and usually just stick around as “ x” and “ y” in the equation. In this equation, the letters h, k, and r are constants - in other words, their values are fixed. Think of this equation as the master template for every possible equation of a circle. The equation of a circle of radius r centered at the point ( h, k)
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