Find Hyperbola equation from non orthogonal asymptotesI am looking for an easy way to find the hyperbola that has two non vertical asymptotes y = m 1 x + q 1 and y = m 2 x + q 2 and with a vertex located at a distance r from the point where the two asymptotes join.Would appreciate any help.

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Find Hyperbola equation from non orthogonal asymptotesI am looking for an easy way to find the hyperbola that has two non vertical asymptotes   y  =      m    1    x  +      q    1   and   y  =      m    2    x  +      q    2   and with a vertex located at a distance r from the point where the two asymptotes join.Would appreciate any help.

Alyvia Marks · Accepted Answer

Every hyperbola with the given lines as asymptotes has equation of the form            [        y  −  (      m          1        x  +      q          1        )            ]                  [        y  −  (      m          2        x  +      q          2        )            ]        =  cfor some real number c. (If c=0 you recover the asymptotes.)If you have a convenient way of getting the coordinates of a vertex (or any point on the hyperbola), evaluating the left-hand side gives c. (There are two pairs of potential vertices at distance r from the point where the asymptotes intersect, lying along the lines bisecting the angles between the asymptotes.)

Find Hyperbola equation from non orthogonal asymptotes I am looking for an easy way to find the hyperbola that has two non vertical asymptotes y=m1x+q1 and y=m2x+q2 and with a vertex located at a distance r from the point where the two asymptotes join. Would appreciate any help.

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