Center of a Circle Solved Examples
Example 1: The task at hand is to determine the radius and center of the circle that is shown by the equation (x−3)2 + (y+2)2 = 25.
Solution:
Given,
(x−3)2 + (y+2)2 = 25
By comparing with the standard form (x − h)2 + (y − k)2 = r2
We determine radius and the center is at,
r = 5
(h, k) = (3, −2)
Example 2: Find the radius and center of the circle that passes through the three points A(1,2), B(5,6), and C(−3,4).
Solution:
Given three non-collinear points, use the formula for the center of a circle:
where h = (x1 + x2 + x3)/3 and k = (y1 + y2 + y3)/3
h = (1 + 5 − 3)/3 = 1
k = (2 + 6 + 4)/3 = 4
Center is at (h, k) = (1, 4).
Use distance formula between center and any of provided points to find the radius.
Example 3: Given the Circle’s Equation: (x − 3)2 + (y + 4)2 = 25.
Solution:
Let us take the case where we have the circle equation (x − 3)2 + (y + 4)2 = 25.
First, determine center coordinates.
Equation allows us to determine center coordinates (h,k) directly:
- h = 3
- k =−4
Thus, (3, -4) is circle’s center.
Center of Circle
Center of a Circle is defined as a point inside the circle that is equidistant from all the points on the circumference of the circle. It is generally denoted using (h, k) points and is the point from where all the radius passes. Cente of the circle is defined as the mid-point of the end point of the diameter of the circle.
In this article, we will learn about, center of a circle, its formulas, and examples in detail.
Table of Content
- What is Centre of a Circle?
- Center of Circle Formula
- How to Find Centre of a Circle?
- How to Find Center of Circle with Two Points?
- How to Express Center of Circle?
- Center of Circle Using Midpoint Formula
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