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Jul 31, 2024 · The equation of a circle is (x-4)² + (y-6)² = 8.You can find this equation by using the following steps: Find the x-coordinate (h) & y-coordinate (k) of the center of the circle by taking the summation of x-coordinates & y-coordinates of the endpoints of the diameter respectively and dividing by 2.
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are and . The center point of the circle is the center of the diameter, which is the midpoint between and . In this case the midpoint is .
10 hours ago · If you know the endpoints of a circle’s diameter, you can derive the center and radius to find other circle properties. Midpoint Formula Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) This gives the center of the circle. Distance Formula Distance = √((x₂ - x₁)² + (y₂ - y₁)²) The radius is half the distance between the diameter ...
The above form of the equation is the general form of the equation of circle. How do you Write the Standard Form of a Circle Equation with Endpoints? Let's take the two endpoints of the diameter to be (1, 1), and (3, 3). First, calculate the midpoint by using the section formula. The coordinates of the center will be (2, 2).
Example calculating midpoint and distance to find the equation of a circle given two endpoints of the diameter.
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This is the equation of the circle through the extremities (ends) of its diameter. In order to find the centre and radius of this circle, we simplify the above equation of a circle as follows: