Conics - Rectangular Hyperbola (1 Viewer)

[RivalryofTroll]

Prove that the hyperbola with equation x^2 - y^2 = a^2 is the hyperbola xy = 1/2.a^2 referred to different axes.

Do you use perpendicular distances or something?

Not sure how to do it.

 

[qrpw]

Take a random point (x1, y1) on the hyperbola, and multiply it by (cis 45) to rotate it anticlockwise. So something like (x1 + iy1)(cis45). Then solve the locus when you get your new x and y-coordinates.

 

[RivalryofTroll]

Take a random point (x1, y1) on the hyperbola, and multiply it by (cis 45) to rotate it anticlockwise. So something like (x1 + iy1)(cis45). Then solve the locus when you get your new x and y-coordinates.

Is there a way to do it without Complex Numbers?

 

[FdashX]

when theres a way of solving with complex numberz
ALWAYS used complex numberz!

complex numberZ ruleZ

 

[asianese]

Look up Terry Lee - utilises perpendicular distances from tangents.