Question

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

Solution

Correct option is

Let the given points lie on the line

      px + qy + r = 0, then

      pt3 + q(t2 – 3) + r(t – 1) = 0

or  pt3 + qt2 + rt – (3q + r) = 0   has roots a, b, c

          

Let us eliminate p, q, r from above

        

SIMILAR QUESTIONS

Q1

The in centre of the triangle with vertices , (0, 0) and (2, 0) is

Q2

If a vertex of a triangle is (1, 1) and the mid-point of two sides through the vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

Q3

If the equation of the locus of a point equidistant from the points

(a1b1) and (a2b2) is (a1 – a1)x + (b1  –  b2)y + c = 0,

Then the value of c is :

Q4

The line joining the point  is produced to the point L(x, y) so that AL : LB b : a, then 

               

Q5

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If and I be the centoid and in center of the triangle, then GI is equal to

Q6

If a, b, c are relation by 4a2 + 9b2 – 9c2 + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

Q7

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the numbers of integral coordinates strictly inside the triangle (integral coordinates of both and y)

Q8

If x1x2x3 as well as y1y2y3 are in G.P. with the same common ratio, then the points (x1y1), (x2y2) and (x3y3)

Q9

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

Q10

Consider three points

              ,

               and

              , then