Find a Cartesian equation for the hyperbola which has asymptotes

and which passes through the origin.

**Incomplete.**

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Stumbling Robot

A Fraction of a Dot
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Find a Cartesian equation for a hyperbola through the origin

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Find a Cartesian equation for the hyperbola which has asymptotes

and which passes through the origin.

**Incomplete.**

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. (Sorry, I noticed that I skipped one excercise and the comments got out of sync with the text…)