Find a Cartesian equation for the parabola which has directrix and whose focus is at the origin.
Incomplete.
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S says:
We can assume that when we shift the asymptotes to (0,0), we will have the hyperbola discussed in section 13.22. Such asymptotes are y = +/-(2x). From that we know that a/b=2 and y^2/a^2 – x^2/b^2 = 1. The shifted hyperbola to those asymptotes goes through (-1/2, -2). We plug in the values and get (y-2)^2 – (2x-1)^2=3, which is the solution in the book.
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and whose focus is at the origin.
We can assume that when we shift the asymptotes to (0,0), we will have the hyperbola discussed in section 13.22. Such asymptotes are y = +/-(2x). From that we know that a/b=2 and y^2/a^2 – x^2/b^2 = 1. The shifted hyperbola to those asymptotes goes through (-1/2, -2). We plug in the values and get (y-2)^2 – (2x-1)^2=3, which is the solution in the book.