
The standard form of a parabola in cartesian coordinates is,
c(t) = t s_{1} + at^{2} s_{2} 

where a > 0 and t Î R.
The standard form of the same parabola in polar coordinates
centered at the focus p is,
x(q) = p + 
L
1+cos(q)

se^{iq} 

where s is a unit vector in the iplane of the parabola. i.e.
s^{2}=1 and sÙi = 0.
Find i,L,s,p,q in terms of a,s_{1},s_{2},t.
Hint: Find the location of the vertex x(q_{0}) where the parabola
has maximum curvature and equate [^v](q_{0}) = s_{2}.
