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Let us remember that for a circle with center ( ℎ, 𝑘 ) and radius 𝑟, the Triangle as shown in the diagram below, where the hypotenuse is a radius of the circle.Įxample 2: Finding the Center and Radius of a Circle from Its Equation in Standard Formįind the center and radius of the circle ( 𝑥 − 2 ) + ( 𝑦 − 8 ) − 1 0 0 = 0  . 𝑥- and 𝑦-coordinates of all the points on the circle can then be found by forming a right On the circle to the origin is thus equal to the radius of the circle, 𝑟. The distance from any point 𝑀 ( 𝑥, 𝑦 ) This circle is the locus of points equidistant from the origin. To understand this equation, let us first of all consider the most basicįorm of a circle: a circle that is centered at the origin of the coordinate plane. On the circle: this is the equation of a circle. However, there does exist a relationship between the 𝑥- and 𝑦-coordinates of all points In other words, we can always find two points on the circle that have the same 𝑥-coordinate. Of the form 𝑦 = 𝑓 ( 𝑥 ) since any one element of the domain can (generally) be associated with twoĮlements of the range. We note that although a circle can easily be plotted on the 𝑥 𝑦-plane, it cannot be described as a function In other words, a circle is the set of all points, and only those, that are at a given distance from its center. This fixed distanceīetween any point of the circle and its center is the radius of the circle. A circle is the locus of points equidistant from a given point, called the center of the circle.