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 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 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 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 points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0