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JEE Main202118 Mar 2021Morning ShiftMathematicsHyperbolaActual

A square A B C D has all its vertices on the curve x 2 y 2 = 1 . The midpoints of its sides also lie on the same curve. Then, the square of area of A B C D is

Correct answer

80

Step-by-step solution

x y = 1 ,   - 1 t 1 + t 2 2 · 1 t 1 - 1 t 2 2 = 1 ⇒ t 2 2 - t 1 = 2 4 t 1 t 2 Product of slope = - 1 1 t 1 2 × - 1 t 2 2 = - 1 ⇒ t 1 t 2 = 1 ⇒ t 1 t 2 2 = 1 ⇒ t 1 t 2 = 1 ⇒ t 1 2 + t 2 2 = 4 2 + 4 = 2 5 ⇒ t 1 2 = 2 + 5 ⇒ 1 t 1 2 = 5 - 2 A B 2 = t 1 - t 2 2 + 1 t 1 + 1 t 2 2 = 2 t 1 2 + 1 t 1 2 = 4 5 ⇒  Area  2 = 80 sq. unit

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