Answered

Consider the parametric equationsx=cost -sint/√2y = cos t + sin t0 < t < 2pia. Eliminate the parameter to find a Cartesian equation for the parametric curve. Hint: Multiply by , 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 :

Answer:

(a)[tex]x^2+2y^2=2[/tex]

(b)In the attached diagram

Step-by-step explanation:

[tex]x=cost -sint\\y\sqrt{2} =cost +sint, 0<t<2\pi[/tex]

Step 1: Multiply both equations by t

[tex]xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)[/tex]

Step 2:We square both equations

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

Step 3: Adding the two equations

[tex](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[/tex]

Other Questions