# mid2s - Name Quiz Section MIDTERM II Math 126 Section C...

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Name Quiz Section MIDTERM II Math 126, Section C November 17, 2006 Problem Total Points Score 1 9 2 15 3 12 4 12 5 12 Total 60 6(Bonus) 2 - You may use a scientific calculator and one two-sided sheet of handwritten notes. No other notes, books or calculators are allowed. Please turn off your cell phone. - Show all your work to get full credit. - Read instructions for each problem CAREFULLY. - Leave all your answers in EXACT form. - Check your work! 1

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1. (9pts) A curve is given by the equation r + 1 r = 4 cos θ in polar coordinates. (a) (7pts) Find the equation of the curve in Cartesian coordinates. Sketch the curve. (b) (2pts) Using your sketch, find all the points on the curve where the tangent line is horizontal. 2
2. (15pts) Consider an ellipse given by the equation ( x - 1) 2 9 + ( y - 1) 2 16 = 1 –2 2 4 –2 –1 1 2 3 4 (a) (5pts) Find parametric equations of the ellipse. (b) (5pts) Set up, but do not evaluate, the integral computing the length of the arc of the ellipse going clockwise from the point (1 , 5) to the point (4 , 1).

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