All these circles are of different sizes and have different radii. In the above figure, there are three circles inside one another. When two or more circles have a common center, then these circles are called concentric circles. When circles meet orthogonally, the length of 1 circle's tangent from the opposite circle's center equals the radius of the opposite circle. Let \[S_) are the respective circle centers, S = zero and S 1 = zero. If k = –1, we will get an equation of the common chord i.e. Further, the parameter value of the parameter gives a unique circle. Again we are left with one parameter (k) equation of the Family of Circles. The general equation of the Family of Circles is passing through the intersection of S 1 and S 2 which is given by S 1 + KS 2 = 0, where k ≠ -1. Equation of Family of Circles passing through the intersection of two circles S 1 = 0 and S 2 = 0. The fixation of the radius will give a particular circle.Ģ. Where (h, k) is fixed and the only parameter that is varying is r. When Family of Circles Have a Fixed Center Let’s discuss some of the ways of finding the family of the circle when you are given certain conditions:ġ. The imposition of a third condition will result in the equation which represents a particular circle. Without the condition, we get the equation of the Family of Circles that satisfies the given two conditions. g, f and c so we require at least three conditions to get a unique circle.įor instance, if we are given two circles and we need to resolve the third circle touching the rest of both the circles.
However, the equation contains three unknown figures i.e. The general equation of the circle can be given as x 2 + y 2 + 2gx + 2fy + c = 0.
The circles consisting of the same properties are combined in various ways to form the Family of Circles. The Family of Circles is one of the most important parts of coordinate geometry in which different circles are present at the same time, through which the calculations to find the values in circles becomes easy. There are various types of circles available around us. A huge collection of circles is called a Family of Circles. A circle is a closed shape in which all the points lying on the surface of the circle joining its center are equal and known as the radius of the circle.
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