If someone could check my work and make sure I'm doing these problems right, I would really appreciate it. 1.Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: [tex] x= h + r cos \theta , y= k + r sin \theta [/tex] [tex] (x-h/r)^2 + (y-k/r)^2 = 1[/tex] 2.Find the arc length of the given curve on the indicated interval. [tex] x=t^2 +1, y=4t^3 + 3 [/tex] [tex] 0 \leq t \leq -1 [/tex] [tex] S= \int \sqrt (dx/dt)^2 + (dy/dt)^2 [/tex] dx/dt= 2t, dy/dt= 12t^2 so i intregrated from -1 to 0, [tex] \int \sqrt 4t^2 +144t^2 dt [/tex] using a u subsitution, I got [tex] 1/432(4+144t^2)^(3/2) [/tex] Plugging in -1 and 0 gave me -4.15, which can't be right since it's talking about arclength.. 3.Convert the rectangular equation to polar. [tex] x^2 + y^2 - 2ax = 0 [/tex] [tex] r^2 = 2ax [/tex] [tex] r^2 / r cos \theta = 2a (r cos \theta)/ r cos \theta [/tex] Solving for r gave me [tex] r= 2a cos \theta [/tex] If these are wrong, any help would be appreciated. Thanks!