Which of the following points lie on the x-axis?
The line joining A(bcosαbsinα) and B(acosβ,asinβ) is produced to the point M(x,y) so that AM and BM are in the ratio b:a˙ Then prove that x+ytan(α+2β)=0.
In ABC, the coordinates of B are (0,0),AB=2,∠ABC=3π, and the middle point of BC has coordinates (2,0)˙ The centroid o the triangle is (21,23) (b) (35,31) (4+33,31) (d) none of these
If x1,x2,x3 as well as y1,y2,y3 are in GP with the same common ratio, then the points (x1,y1),(x2,y2), and (x3,y3)˙ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.
Find the coordinates of the points which divide the line segment joining A(2,2)andB(2,8) into four equal parts.
If (acosθ1,asinθ1),(acosθ2,asinθ2) and (acosθ3,asinθ3) represent the vertices of an equilateral triangle inscribed in a circle, then (a) cosθ1+cosθ2+cosθ3=0 (b) sinθ1+sinθ2+sinθ3=0 (c) tanθ1+tanθ2+tanθ3=0 (d) cotθ1+cotθ2+cotθ3=0
Two points PandQ are given. R is a variable point on one side of the line PQ such that ∠RPQ−∠RQP is a positive constant 2α˙ Find the locus of the point R˙