8 July 20 1. 92.450 / 550 Math Modeling Due y (a) Find the curve with the property that light rays emanating from the point (a , 0) are reflected to the point (a , 0). r Hint. This is similar to the parabola problem in class . . . Use r1 r2 and r2 instead of r and . 1 (b) Show |r | r +| 1 | a is the same regardless of the path taken. x 2 q 2. 3. What is the solution of the brachistochrone problem if v = 2 2g y ? (a) Find (x , t ) in the fan region for the initial condition 0 , x < 0 0 (x , 0) = 0, 0 (1 x /L ),x > L x L using the quadratic velocity-density function u () = u 0 1 2 / 2 , 0 0 . (b) Put L = 0 in (a) and find the solution of the car equation d X /d t = u () in the fan. a