How to Derive the Diameter Equation of a Circle
Learn to derive the diameter equation of a circle using the midpoint and distance formulas.
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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
- 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.
- 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.
- 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.
- 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.