If `sum_(i-1)^4(xi2+y i2)lt=2x_1x_3+2x_2x_4+2y_2y_3+2y_1y_4,` the points `(x_1, y_1),(x_2,y_2),(x_3, y_3),(x_4,y_4)` are the vertices of a rectangle collinear the vertices of a trapezium none of these

If x_1 , x_2, x_3 as well as y_1, y_2, y_3 are in A.P., then the points (x_1, y_1), (x_2, y_2), (x_3, y_3) are (A) concyclic (B) collinear (C) three vertices of a parallelogram (D) none of these

The area of the Quadrilateral with vertices A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) and D(x_(4),y_(4)) is

Four points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) and (x_(4),y_(4)) are such that sum_(i=1)^(4)(x_(i)^(2)+y_(i)^(2))<=2(x_(1)x_(3)+x_(2)x_(4)+y_(1)y_(2)+y_(3)y_(4)) Then these points are vertices of - (A) Parallelogram (B) Rectangle (C) Square (D) Rhombus

If the points (x_1,y_1),(x_2,y_2)and(x_3,y_3) are collinear, then the rank of the matrix {:[(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)]:} will always be less than

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