write an equation in standard from of a hyperbola

Question

How to write an equation in standard form of a hyperbola given center (0,0), transverse: x-axis, asymptotes: y=x and y=-x

Answer 1

sounds so standard maybe xy=1? but rotated 45 degrees

rectangular hyperbola with asymptotes x=0, y= 0, both axes rotated 45 degrees

immediare guess is xy =-1

wouldn't hurt to try graphing the equations

desmos, an online or hand held calculator can do it for you

Nope that didn't work.

that was a 90 degree rotation, try for half that

or try x^2-y^2 = 2

or x^2 -y^2 = any constant

the graph looks very convincing that the asymptotes are 45 degree angles from the x and y axes