How to Derive the Diameter Equation of a Circle

Learn to derive the diameter equation of a circle using the midpoint and distance formulas.

13 views

The equation of the diameter of a given circle can be easily derived if you know the center and a point on the circle. Suppose the circle’s center is at coordinates (h, k) and a point on the circle is (x1, y1). The midpoint formula can be used: (x1 + h)/2, (y1 + k)/2 to find the midpoint, which is the center, confirming the diameter. To find the length, use the distance formula between these points: D = 2 * sqrt((x1 - h)^2 + (y1 - k)^2).

FAQs & Answers

  1. What is the formula for the diameter of a circle? The diameter can be found using D = 2 * sqrt((x1 - h)^2 + (y1 - k)^2), where (h, k) is the center and (x1, y1) is a point on the circle.
  2. How do you find the center of a circle? The center of a circle can be located using the midpoint formula if you have the coordinates of two points on the circle.
  3. What is the difference between radius and diameter? The radius is half the length of the diameter; the diameter goes through the center and touches two points on the circle.
  4. What does the equation of a circle look like? The standard equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.