Rectangular Hyperbola

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JEE Advanced 1998

If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $x y = c^{2}$ in four points $P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4})$ , then

* Multiple Correct Options

x_{1} + x_{2} + x_{3} + x_{4} = 0

y_{1} + y_{2} + y_{3} + y_{4} = 0

x_{1} x_{2} x_{3} x_{4} = c^{4}

y_{1} y_{2} y_{3} y_{4} = c^{4}

JEE Main 2021 (18 March Shift 1)

LEVELJEE Advanced

A square ABCD 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 ABCD is

JEE Main 2023 (11 Apr Shift 1)

Let $R$ be a rectangle given by the lines $x = 0, x = 2, y = 0$ and $y = 5$ . Let $A (α, 0)$ and $B (0, β)$ , $α \in [0, 2]$ and $β \in [0, 5]$ , be such that the line segment $A B$ divides the area of the rectangle $R$ in the ratio $4 : 1$ . Then, the mid-point of $A B$ lies on a