Question

INSANE IMPOSSIBLE QUESTION 100%?!? WORLD RECORD GLITCHED POST!!!

A hyperbola of x^2 - y^2 = 1 has 2 asymptotes.
If we were to apply a linear transformation to the equation, would the asymptote transform the same way?
T(x,y) = (3x-2,4y+1)
Asymptot: y = x and y = -x

Answer 1

Sketch those lines slopes of +/- 1

center axis halfway between 1 and 5 so at y = 3
the lines cross at (2,3), so that is center of hyperbola
so
(x-2)^2/a^2 - (y-3)^2/b^2 = 1
slopes of asymptotes = +/- b/a so b = a

(x-2)^2/a^2 - (y-3)^2/a^2 = 1
put that point in now
(4-2)^2/a^2 - (3-3)^2/a^2 = 1
a^2 = 4
a = 2
(x-2)^2/4 - (y-3)^2/4 = 1

Answer 2

Thanx so much

Answer 3

NP @mhchen