Question

 

If the orthocentre of the triangle formed by the lines

2x + 3y – 1 = 0, x + 2y – 1 = 0, ax + by – 1 = 0   is at origin, then find (a,b).

Solution

Correct option is

(–8, 8)

 

The equation of a line through A i.e., the point of intersection of AB andAC, is  

           

It passes through O(0, 0), then                  

    –1 – λ = 0     

  

From eq. (i), 

       

  

Since   AD ⊥ BC

    

    

  

Similarly,   BC ⊥ AC, we get         

       a + b = 0                             … (iii) 

Solving eqs. (ii) and (iii), we get   

       b = 8 and a = –8     

∴    (ab) is (–8, 8)

SIMILAR QUESTIONS

Q1

Find the equations of the line parallel to 5x – 12y + 26 = 0 and at a distance of 4 units from it.

Q2

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 (ab and cbeing distinct and difference from 1) are concurrent, then find the value of

Q3

Find the equation of the straight line passing through the point (2, 1) and through the point of intersecction of the lines x + 2y = 3 and 2x – 3y = 4.

Q4

The family of lines x(a + 2b) + y(+ 3b) = b passes through the point for all values of a and b. Find the point.

Q5

If 3a + 2b + 6c = 0 the family of straight lines ax + by + c = 0 passes through a fixed point. Find the coordinates of fixed point.

Q6

 

Find the equation of the line passing through the point of intersection of the lines

          x + 5y + 7 = 0, 3x + 2y – 5 = 0 and   

1. parallel to the line 7x + 2y – 5 = 0

2. perpendicular to the line 7x + 2y – 5 = 0

Q7

 

Find the equation of straight line which passes through the intersection of the straight lines  

        3x – 4y + 1 = 0 and 5x + y – 1 = 0 

and cuts off equal intercepts from the axes.

Q8

Find the orthocentre of the triangle of the triangle ABC whose angular points are A(1, 2), B(2, 3) and C(4, 3).  

Q9

Find the equations of the straight lines passing through the point (2, 3) and inclined at π/4 radians to the line 2x + 3y = 5.

Q10

 

Find the equations to the straight lines passing through the point (2, 3) and equally inclined to the lines 3x – 4y – 7 = 0 and

12x – 5y + 6 = 0