Question
consider the graph of the equation xy=9. rotate the graph 45 degrees clockwise about the center (0,0). what is the equation of the rotated graph?
Answers
Reiny
the rotation matrix is
⎡cos45 -sin45⎤
⎣sin45 cos45 ⎦
⎡√2/2 - √2/2⎤
=⎣√2/2 √2/2⎦
multiply this by
⎡x⎤
⎣y⎦
gave me
x' = √2/2 x - √2/2 y
y' = √2/2 x + √2/2 y
subbing that into xy=9
(√2/2 x - √2/2 y)(√2/2 x + √2/2 y) = 9
2x^2/4 - 2y^2/4 = 9
x^2 - y^2 = 18
⎡cos45 -sin45⎤
⎣sin45 cos45 ⎦
⎡√2/2 - √2/2⎤
=⎣√2/2 √2/2⎦
multiply this by
⎡x⎤
⎣y⎦
gave me
x' = √2/2 x - √2/2 y
y' = √2/2 x + √2/2 y
subbing that into xy=9
(√2/2 x - √2/2 y)(√2/2 x + √2/2 y) = 9
2x^2/4 - 2y^2/4 = 9
x^2 - y^2 = 18