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A tangent to the hyperbola x²/4 - y²/2 = 1 meets the x-axis at P and the y-axis at Q. Points R is chosen so that OPRQ is a rectangle (O is the origin). Find the curve on which R lies.

1. 4/x² - 2/y² = 1
2. 2/x² - 4/y² = 1
3. 4/x² + 2/y² = 1
4. 2/x² + 4/y² = 1

Correct answer: 4/x² - 2/y² = 1

Solution

The intercepts give X = 2*cos(t) and Y = -sqrt(2)*cot(t); eliminating t yields 4/X² - 2/Y² = 1.

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