Question

If A (cos α, sin α), B (sin α, –cos α), C (1, 2) are the vertices of a ΔABC, then as α varies the locus of its centroid is:

Solution

Correct option is

3 (x2 + y2) – 2x – 4y + 1 = 0

Suppose co-ordinate of centroid is (x1y1)

   

    

  

Square and add (i) and (ii)

  

Replace x1 by x and y1 by y.     

SIMILAR QUESTIONS

Q1

Find the equation of the straight line passing through the points (3, 3) and (7, 6). What is the length of the portion of the line intercepted between the axes of the coordinates.

Q2

Given the triangle with vertices A (–4, 9), B (10, 4), C (–2, –1). Find the equation of the altitude through A.

Q3

Find the equation of perpendicular bisector of the line joining the points (1, 1) and (2, 3). 

Q4

Find the coordinates of the foot of the perpendicular from the point (2, 3) on the line y = 3x + 4.

Q5

Find the equation of the line passing through (ab) and parallel to px +qy + 1 = 0.  

Q6

Find the equation of the line perpendicular to 3x + 4y + 1= 0 and passing through (1, 1).

Q7

Find the distance of line h (x + h) + k (y + k) = 0 from the origin.

Q8

Determine the distance between the lines : 6x + 8y – 45 = 0 and 3x + 4y – 5 = 0.

Q9

The algebraic sum of the perpendicular distances from A(x1y1), B(x2,y2) and C(x3y3) to a variable line is zero, then the line passes through:

Q10

The image of point (1, 3) in the line x + y – 6 = 0 is: