Question

Consider the parametric equations

x = cos(2t) - sin(2t), y= cos(2t) + =sin(2t t <

a. Eliminate the parameter t to find a Cartesian equation for the parametric curve.

Hint: Multiply y by v2, then square both equations and add them together.

b. Sketch the parametric curve, indicating with arrows the direction in which the curve is traced.

Answer 1

Answer:(a)x^2+2y^2=2

(b)In the attached diagram

Step-by-step explanation:Step 1: Multiply both equations by t

xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)

Step 1: Multiply both equations by t

xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)

Step 2:We square both equations

(xt)^2=t^2(cost -sint)^2\\(ty)^2(\sqrt{2})^2 =t^2(cost +sint)^2

Step 3: Adding the two equations

(xt)^2+(ty)^2(\sqrt{2})^2=t^2(cost -sint)^2+t^2(cost +sint)^2\\t^2(x^2+2y^2)=t^2((cost -sint)^2+(cost +sint)^2)\\x^2+2y^2=(cost -sint)^2+(cost +sint)^2\\(cost -sint)^2+(cost +sint)^2=2\\x^2+2y^2=2 hopes this helps