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) 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)

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 1) x_(1)+x_(2)+x_(3)+x_(4)=2c^(2) 2) y_(1)+y_(2)+y_(3)+y_(4)=0 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) 4) y_(1)y_(2)y_(3)y_(4)=2c^(4)

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 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

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) 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