Question

If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is

Solution

Correct option is

Let the coordinate of the center of mean position of the points

      Ai, i = 1, 2 …n be (x, y), then

        

     

SIMILAR QUESTIONS

Q1

If a (2,0) and (0,2) are given points and p is a point such that PA:PB = 2:3 then the locus of p passes through the point (a,a) for

Q2

A(1, 3), B(3, 7) & C(7, 15) are three points. P is the midpoint of ABQ is the midpoint of BC. Locus of a point R which satisfies (PR)2 – (QR)= (AC)2 is

Q3

If A(1, a), B(a, a2), C(a2, a2) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point

Q4

Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is

Q5

Coordinate (x, y) of a point P satisfy the relation 3x + 4= 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is

Q6

The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 

Q7

Q, R and are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.

Q8

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

Q9

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

Q10

If α, β, γ are the real roots of the equation x3 – 3px3 + 3qx – 1 = 0, then the centroid of the triangle with vertices