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 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 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 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 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 point (x_i,y_i) for i=1,2,3, and 4 then y_1+ y_2 +y_3 +y_4 =