**Question:**

A particular planar ellipse in 3-space is parametrized by r(t) =< 10 cos t, sin t, 10 >.

a) What is the equation of the plane in which the ellipse lies?

b) Find the curvature of ellipse at any value of t.

c) Find curvature of ellipse at points P (10, 0, 10) and Q(0, 1, 10).

d) At which points in part c, the curvature bends rapidly.

**Solution:**

a) Tangent vector to the ellipse is given by,

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