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Astroid. Cartesian Equation: y. x2=3 + y2=3 = a2=3. Parametric Equations: x(t) = a cos3 t. y(t) = a sin3 t. PSfrag replacements. a. ¡a a x. Facts: Also called the tetracuspid because it has four cusps. Curve can be formed by rolling a circle of radius a=4 on the inside of a circle of radius a.
16 Νοε 2022 · Here is a set of practice problems to accompany the Parametric Equations and Curves section of the Parametric Equations and Polar Coordinates chapter of the notes for Paul Dawkins Calculus II course at Lamar University.
curve. Problems 1. Consider the curve parametrized by x(θ) = acosθ, y(θ) = bsinθ. (a) Plot some points and sketch the curve when a= 1 and b= 1, when a= 2 and b= 1, and when a= 1 and b= 2. (b) Eliminate the parameter θto obtain a single equation in x, y, and the constants aand b. What curve does this equation describe? (Hint: Eliminate ...
2 (**+) The curve C has equation. y = ( x − a )2 + b , where a , b are positive constants. By considering the two transformations that map the graph of y = x 2 onto the graph of C , or otherwise, sketch the graph of C . The sketch must include the coordinates, in terms of a , b , of ...
29 Δεκ 2020 · When a curve lies in a plane (such as the Cartesian plane), it is often referred to as a plane curve. Examples will help us understand the concepts introduced in the definition.
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;
1. The cartesian equation of the circle C is. x2 + y2 – 8x – 6y + 16 = 0. Find the coordinates of the centre of C and the radius of C. Sketch C. (4) (2) (c) Find parametric equations for C. (3) (d) Find, in cartesian form, an equation for each tangent to C which passes through the origin O. (5) (Total 14 marks) 2.
