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.

Cristal Travis

Cristal Travis

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2022-08-21

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 = 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.

Answer & Explanation

Alyvia Marks

Alyvia Marks

Beginner2022-08-22Added 12 answers

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 ) ] = c
for 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.)

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