Rectangular Car...

If O be the origin and if the co-ordinates of any two points Q₁ and Q₂ be (x₁, y₁) and (x₂, y₂) respectively. Then OQ₁ ∙ OQ₂ cos Q₁OQ₂ =

Given the points A(0,4) and B(0,4). Then the equation of the locus of the point P(x,y) such that |AP - BP) = 6 is

If ABCD is a quadrilateral, if the mid point of consecutive sides AB, BC, CD and DA are combined by straight lines, then the quadrilateral PQRS is always

A(a,0) and B(-a,0) are two fixed points of triangle ABC. The vertex C moves in such a way that cot A + cot B = λ , where λ is a constant.Then the locus of the point C is

A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is the same, then in the ∆ABC, the foot of the pole is at the

The point A divides the join of the points (-5,1) and (3,5) in the ratio k : 1and the co-ordinates of the points B and C are (1,5) and (7,-2) respectively. If the area of the triangle ABC be 2 units , then k =

The area of a triangle is 5. If two of its vertices are (2,1), (3,-2) and the third vertex lies on the line y = x + 3, then the third vertex is

P(3,1) , Q(6,5) and R (x,y) are three points such that the angle PRQ is a right angle and the area of the ∆RPQ = 5, then the number of such points R is

The points P is equidistant from A(1,3) , B(-3,5) and C(5,-1). Then PA =