Question

A and B are two fixed points. The vertex C of a Δ ABC moves such that cot A + cot B = constant. Locus of C is a straight line:

Solution

Correct option is

Parallel to AB

It is given that point A and B are fixed. Only point C is moving.

And also cot A + cot B = constant = k

  

  

C lies on a line which is always at a distance P from AB.

Hence, locus of C is a straight line parallel to AB.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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:

Q7

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:

Q8

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

Q9

If t1t2t3 are distinct, then the points  are collinear if:

Q10

The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is: