(a) A car is driving on a circular lane with a radius of 1 (km). At the southernmost point of the course is a radar meter. At a given time, the car is 1/2 km from the meter and the distance between the car and the meter increases by 50 km / h. How fast is the car driving north?  (b) A curve is given by x cos (πxy) = x + y + 1. Find the tangent and normal of the curve at the point (0, −1).

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