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Unformatted text preview: MATH. 222, LEC. 3, EXAM #3 YOUR NAME
T.A.'s NAME Show all your work. No calculators or references. I 2.(20 pts) 390 pts) 1. Name the conic described by 2y2  x2  8y + 2x + 5 = O. .
' Sketch the graph of the equation and ﬁnd the eccentricity;
and the vertices. 2. (a) Name the conic described (in polar coordinates) by
r = 2/(2 + cos(@ D. '
(b)Draw a sketch of the curve.
(c) Find the eccentricity and the cartesian coordinates of
the vertices. ’ 3. Find the cartesian coordinates of all the intersection points of
the two curves described in polarvcoordinates by r = 1 + cos (9) and r =1 cos(e ). ' 4. Find the unit tangent and curvature of 1'3: et?+ eZt/j‘ at the,
point t = O. ‘ 5. The position of a particle at time t is given by
ﬁt) = 2t3'i‘+ 3t2’j?  
At time t = 1 ﬁnd the (a) velocity, (b) speed, (c) acceleration,
(d) the tangential component of the acceleration, and
(e) the normal component of acceleration. ...
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 Fall '08
 Wilson
 Calculus, Polar coordinate system, 20 pts, T.A., 390 pts

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