Question

The locus of the mid-point of te portion intercepted between the axes by the line  where is constant is

Solution

Correct option is

Let the line  meet the x-axis and y-axis respectivelyA and B. then coordinates of A are  and those of B are . If (h, k)is the mid-point of AB, then

                     

To find the locus of (h, k) we have to eliminate . We have

              

And        

Whence squaring and adding, we get

                     .

   the required locus of (h, k) is

      

or     

SIMILAR QUESTIONS

Q1

The three lines 4x – 7y + 10 = 0, x + y = 5 and 7x + 4y = 15 from the sides of a triangle. The line (1, 2) is its

Q2

The equation to the side of a triangle are x – 3y = 0, 4x + 3= 5 and 3x + y = 0. The line 3x – 4y = 0 passes through 

Q3

One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is

Q4

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is

Q5

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is

Q6

Area of Δ formed by line x + y = 3 and  bisectors of pair of straight lines x2 – y2 +2y = 1is

Q7

The equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from the axes will be

Q8

The three lines 3x + 4y + 6 = 0,  and 4x + 7y + 8 = 0 are

Q9

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and qpasses through the point

Q10

The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance 2 unit from the origin has the equation