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 which of the following need not hold.
(a)  `x_1+x_2+x_3+x_4=0`
(b)  `x_1 x_2 x_3 x_4=y_1 y_2 y_3 y_4=c^4`
(c)  `y_1+y_2+y_3+y_4=0`
(d)  `x_1+y_2+x_3+y_4=0`

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then

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)) and S(x_(4),y_(4)) then

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 which of the following need not hold. (a) x_(1)+x_(2)+x_(3)+x_(4)=0 (b) x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=c^(4) (c) y_(1)+y_(2)+y_(3)+y_(4)=0 (d) x_(1)+y_(2)+x_(3)+y_(4)=0

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 which of the following need not hold. (a) x_(1)+x_(2)+x_(3)+x_(4)=0 (b) x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=c^(4) (c) y_(1)+y_(2)+y_(3)+y_(4)=0 (d) x_(1)+y_(2)+x_(3)+y_(4)=0

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

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

If the circle x^2+y^2=a^2 intersects the hyperbola x y=C^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then proove x_1+x_2+x_3+x_4=0 , y_1+y_2+y_3+y_4=0 , x_1x_2x_3x_4=C^4 , y_1 y_2 y_3 y_4 = C^4

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) at four points P(x_(1),y_(1)),Q(x_(2),y_(2)),R(x_(3),y_(3)), and S(x_(4),y_(4)), then x_(1)+x_(2)+x_(3)+x_(4)=0y_(1)+y_(2)+y_(3)+y_(4)=0x_(1)x_(2)x_(3)x_(4)=C^(4)y_(1)y_(2)y_(3)y_(4)=C^(4)