The coordinates of the center of the circle represent the distance of the center point from the x-axis and y-axis respectively. What are the Coordinates for the Center of the Circle and the Length of the Radius? In a circle, the distance between the center to any point on the circumference is always the same which is called the radius of the circle. It is the mid-point of the diameter of the circle. The center of a circle is the point where we place the tip of our compass while drawing a circle. Therefore, the coordinates of the center of a circle with the endpoints of diameter are (2, 10).Ĭheck these interesting articles related to the concept of center of circle in geometry.įAQs on Center of Circle What is the Center of Circle? Let us take an example of a circle in which the endpoints of a diameter are given as (-2, 4), and (6, 16). Step 3: Simplify it and get the coordinates of the center of the circle.Step 2: Use the midpoint formula which says that if (h, k) are the coordinates of the midpoint of a segment with endpoints (x 1, y 1) and (x 2, y 2), then (h, k) = /2, /2).Step 1: Assume that the coordinates of the center of the circle are (h, k).The steps to find the center of a circle with two points are given below: If the endpoints of the diameter of the circle are given, then to find the coordinates of the center we use the mid-point formula, because the center is the mid-point of the diameter of the circle. How to Find the Center of Circle with Two Points? So, we have got the coordinates of the center of circle which are (h, k) = (2, 3). If we compare (x - 2) 2 + (y - 3) 2 = 10 2 with (x - h) 2 + (y - k) 2 = r 2, we can identify that h = 2, k = 3, and r = 10. Step 2: Compare this equation with the general equation and identify the values of h, k, and r.This looks like the general equation of circle. So, we will get, x 2 - 4x + 4 + y 2 - 6y = 87 + 4.Īdd 9 to both sides to get a perfect square of y - 3 Add 4 to both sides of the equation to get a perfect square of x-2. We can write the given equation as x 2 - 4x + y 2 - 6y = 87.
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