A circle is all points in a plane that are a fixed distance from a given point in the plane. The given point is called the center, (h,k) (h, k), and the fixed distance is called the radius, r r, of the circle. To derive the equation of a circle, we can use the distance formula with the points (h,k) (h, k), (x,y) (x, y), and the distance r r.

2022年7月13日 · The circle can be represented by \(x^{2} +y^{2} =50^{2}\). Finding a line from (0,60) to (70,0) gives \(y=60-\dfrac{60}{70} x\). Substituting the line equation into the circle gives \(x^{2} +\left(60-\dfrac{60}{70} x\right)^{2} =50^{2}\). Solving this equation, we find \(x = 14\) or \(x = 45.29\), corresponding to points (14, 48) and (45.29, 21 ...

2023年11月28日 · The general equation of a circle is (x − h) 2 + (y − k) 2 = r 2 where (h, k) is the center of the circle and r is the radius of the circle. You can derive the equation of a circle with the help of the Pythagorean Theorem. 1. Label the three sides of …

A circle is easy to make: Draw a curve that is radius away from a central point. And so: All points are the same distance from the center. x2 + y2 = 52.

Area of Part of a Circle Given a circle of radius a, cut out a tab of height b. What is the area of this tab? (See Figure 1.) (0,b) (a, 0) Figure 1: Tab cut out of a circle. One way to compute the area would be split the area into vertical strips and integrate with respect to x: Area = y dx.

2025年1月31日 · A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. Twice the radius is known as the diameter d=2r.

2022年11月16日 · A circle is all the points that are the same distance, \(r\) – called the radius, from a point, \(\left( {h,k} \right)\) - called the center. In other words, if \(\left( {x,y} \right)\) is any point that is on the circle then it has a distance of \(r\) from the center, \(\left( {h,k} \right)\).

2013年2月21日 · Defines all points in 2-dimensions that are equal in distance from a given location. A circle is the collection of points that are the same distance from a single point. What is the connection between the Pythagorean Theorem and a circle? The single point that all the points on a circle are equidistant from is called the center of the circle.

2024年12月24日 · This section introduces radian measure and its relationship to arc length in a circle. It explains how radians provide a natural way to measure angles through the context of the circle's radius, enhancing understanding of circular motion and geometry.

2024年12月24日 · This section introduces lines, circles, and angles within the rectangular coordinate system, focusing on the calculation and interpretation of slopes, equations of lines, the distance formula, and the equation of a circle.