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Objectives. After studying this chapter you should. be familiar with cartesian and parametric equations of a curve; be able to sketch simple curves; be able to recognise the rectangular hyperbola; be able to use the general equation of a circle;
EXAMPLE 1.3 Parametric Equations Involving Sines and Cosines Sketch the plane curve defined by the parametric equations x = 2cos t, y = 2sin t, for (a) 0 ≤ t ≤ 2 π and (b) 0 ≤ t ≤ π.
C4 Coordinate geometry - Parametric curves PhysicsAndMathsTutor.com. 1. The cartesian equation of the circle C is . x2 + y2 – 8x – 6y + 16 = 0. (a) Find the coordinates of the centre of C and the radius of C. (4) (b) Sketch C. (2) (c) Find parametric equations for C. (3)
Parametric Curves 17.3 Introduction In this Section we examine yet another way of defining curves - the parametric description. We shall see that this is, in some ways, far more useful than either the Cartesian description or the polar form. Although we shall only study planar curves (curves lying in a plane) the parametric description can
pieces of smooth simple curves. See more from Examples of parametric curves below. Example 1.1. A graph of a function, say y = f(x), is a curve in R2. It has the property that for every x, there is a unique corresponding y (However, there are many curves which do not satisfy this property, and the parametric curves is a generalization which ...
A curve is defined by the following parametric equations x at= 4 2, y a t= +(2 1), t∈ . where a is non zero constant. Given the curves passes through the point A(4,0), find the value of a. a = 4
Locate points on a Cartesian Coordinate System. Discuss the four quadrants of a Cartesian Coordinate System. Identify the x-axis, the y-axis, and the origin on a Cartesian Coordinate System.
