Equation of a Circle
Brightstorm・2 minutes read
Calculate the distance from point HK to XY in a circle with radius R centered at H and K using the distance formula, resulting in the equation R^2 = (x - h)^2 + (y - k)^2. H represents the x-coordinate of the center, K represents the y-coordinate of the center, and R is the radius.
Insights
- The distance formula for a circle in Geometry, R^2 = (x - h)^2 + (y - k)^2, allows for the calculation of the radius R by finding the square root of the sum of squared differences between the x and y coordinates of the center (H, K) and a point (x, y) on the circle.
- Understanding the equation of a circle, R^2 = (x - h)^2 + (y - k)^2, provides a fundamental tool in Geometry to determine the relationship between the center coordinates (H, K), the radius (R), and any point (x, y) on the circle, enabling precise geometric calculations and constructions.
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Recent questions
How do you calculate the distance from a point to a circle?
By using the distance formula: the square root of (x - h)^2 + (y - k)^2.
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Summary
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Calculating Distance in Geometry Circles
- To describe a circle centered at H and K with radius R in Geometry, calculate the distance from point HK to XY using the distance formula: the radius equals the square root of (x - h)^2 + (y - k)^2, leading to the equation of a circle as R^2 = (x - h)^2 + (y - k)^2, where H is the x-coordinate of the center, K is the y-coordinate of the center, and R is the radius.
