Suppose you have a parabola with the directory x y = mx + b and the focus (p, q). Then the equation

Suppose you have a parabola with the directory x y = mx + b and the focus (p, q). Then the equation of that parabola can be written as x2 + Bxy + Cy2' + Dx + Ey + F = 0 where B= C= D = ,and E = F = Your answers will of course be expressions in m, b, p, and q. Utilizing the solution of problem 26 on home work set 1, and the textbook definition of a parabola, this will be mostly an exercise In algebra. The point of the exercise is to illustrate how nice it is to be able to pick the coordinate system, as we did in class. Compare the complexity of the above equation with the equation y2 = 4px that wc used in class.

 

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