SOLUTION: Given the hyperbola xy = 1. Determine the new equation of this hyperbola if the x,y axes are rotated about the origin by 45 degrees clockwise. Answer: y^2 - x^2 = 2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Given the hyperbola xy = 1. Determine the new equation of this hyperbola if the x,y axes are rotated about the origin by 45 degrees clockwise. Answer: y^2 - x^2 = 2      Log On


   



Question 1199546: Given the hyperbola xy = 1. Determine the new equation of this hyperbola if the x,y axes are rotated about the origin by 45 degrees clockwise.
Answer: y^2 - x^2 = 2

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The transformation for a clockwise rotation through an angle A
about the origin is:
x' = xcos(A) + ysin(A)
y' = -xsin(A) + ycos(A)
In this case, A = 45 deg, so the transformed coordinates are:
x' = x/sqrt(2) + y/sqrt(2)
y' = -x/sqrt(2) + y/sqrt(2)
x'*y' = -x^2/2 + y^2/2 = 1 -> y^2 - x^2 = 2