If someone could check my work and make sure I'm doing these problems right, I would really appreciate it.(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Polar & parametric equations

**Physics Forums | Science Articles, Homework Help, Discussion**