Engineering Board Exam Reviewer · Conic Sections and Transformation of Axes · hard
The axes are rotated through 45°. Find the equation of xy=8 in terms of the new coordinates x' and y'.
- x'2+y'2=16
- x'2-y'2=8
- x'2-y'2=16
- x'2-y'2=32
Answer
C. x'2-y'2=16
Solution
Use x=x'-y'/ 2 and y=x'+y'/ 2. Then xy=x'2-y'2/2=8 x'2-y'2=16.
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