If the circle `x^2 + y^2 = a^2` intersects the hyperbola `xy=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 : (A) `x_1 + x_2 + x_3 + x_4 = 0` (B) `y_1 + y_2 + y_3 + y_4 = 0` (C) `x_1 x_2 x_3 x_4= c^4` (D) `y_1 y_2 y_3 y_4 = c^4`

Options

A. `x_1+x_2+x_3+x_4=0`
B. `y_1+y_2+y_3+y_4=0`
C. `x_1x_2x_3x_4=2c^4`
D. `y_1y_2y_3y_4=2c^4`

Answer

A, B, C, D