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The curve xy = 8 is rotated by turning the axes through 45°. Its new equation is
Ax'² - y'² = 16
Bx'² - y'² = 8
Cy'² - x'² = 16
Dx'² + y'² = 16
Answer & Solution
Correct answer: A. x'² - y'² = 16
Substituting x = (x' - y')/√2 and y = (x' + y')/√2 gives xy = (x'² - y'²)/2 = 8, so x'² - y'² = 16.
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