![]() Does the circle intersect the axes? Explain your reasoning. Substitute □ = 1 and □ = 4 into the equation of the circle found in part a.Ĭ. Show that the point with coordinates (1, 4) lies on the circumference of this circle. The radius squared is 9, so the radius is 3 units.ī. Put this all back into the original equation, collect the constants and rearrange into the equation for a circle: The □ terms are □ 2 + 4□ so begin by writing this expression in completed square form: Find the coordinates of the centre and the radius of the circle.Ī. If a question does not give the equation of a circle in this form, you will need to complete the square for □ and □ to convert it to the general form.Ī circle has equation □ 2 + 4□ + □ 2 – 8□ + 11 = 0.Ī. This gives the equation for a circle with a centre at (□, □) and a radius of □: To move the centre □ up, we replace □ 2 with (□ – □) 2.To move the centre □ to the right, we replace □ 2 with (□ – □) 2.You can generalise this to find the equation of a circle with a centre at any point by applying a transformation to the above graph. Which of the following is a chord, but not a diameter?ĥ.Are you looking for info on circles (Maths revision for A level)? A circle, with a centre at the origin and a radius of □, can be described with the equation: A circle divides the plane into three parts: The points inside the circle, the points outside the circle and the points on the circle.ġ. A plane is a flat surface that extends without end in all directions. All diameters are chords, but not all chords are diameters. The parts of a circle include a radius, diameter and a chord. Summary: A circle is a shape with all points the same distance from its center. Solution: The diameter of a circle is twice as long as the radius. If DG is 5 inches long, then how long is DB? Name two chords on this circle that are not diameters. You can see an interactive demonstration of this by placing your mouse over the three items below.Ī circle divides a plane into three parts: The top of your desk and a chalkboard are objects which can be used to represent a plane, although they do not satisfy the definition above.Ī circle divides the plane into three parts: Intuitively, a plane may be visualized as a flat infinite sheet of paper. In the diagram to the right, Plane P contains points A, B and C.Ĭan you think of some real world objects that satisfy the definition of a plane? At this level of mathematics, that is difficult to do. Thus we have circle A.Ī plane is a flat surface that extends without end in all directions. ![]() In the circle to the right, the center is point A. A circle is the set of points that are equidistant from a special point in the plane. Let's revisit the definition of a circle. Thus, it can be stated, every diameter is a chord, but not every chord is a diameter. This is because every diameter passes through the center of a circle, but some chords do not pass through the center. A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter. It turns out that a diameter of a circle is the longest chord of that circle since it passes through the center. By cutting along chord AB, you are cutting off a segment of pizza that includes this chord. If this circle was a pizza pie, you could cut off a piece of pizza along chord AB. The circle to the right contains chord AB. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. As you can see, a circle has many different radii and diameters, each passing through its center.Ī chord is a line segment that joins two points on a curve. A straight cut made from a point on the circle, continuing through its center to another point on the circle, is a diameter. A radius is formed by making a straight cut from the center to a point on the circle. Look at the pizza to the right which has been sliced into 8 equal parts through its center. We can look at a pizza pie to find real-world examples of diameter and radius. Thus, the diameter of a circle is twice as long as the radius. If you place two radii end-to-end in a circle, you would have the same length as one diameter. The radius of a circle is the distance from the center of a circle to any point on the circle. A real-world example of diameter is a 9-inch plate. The distance across a circle through the center is called the diameter. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin. Thus, the circle to the right is called circle A since its center is at point A. We will also examine the relationship between the circle and the plane.Ī circle is a shape with all points the same distance from its center. Let's look at the definition of a circle and its parts. A circle is an important shape in the field of geometry.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |