Question

Find the curvature of each of the functions defined by the parametric equations in Exercises 36–38.

$x=a\cos t,y=b\sin t$

Short answer

The curvature is$\frac{ab}{{\left(a^2{\sin }^{2}t+b^2{\cos }^{2}t\right)}^{\frac{3}{2}}}.$

Step-by-step solution

Step 1. Given information.

The given equations are,

$x=a\cos t,y=b\sin t$

Step 2. Curvature.

Curvature is given by,