Question

The orthocentre of the triangle formed by the pair of lines  and the line x + y + 1 = 0 is 

Solution

Correct option is

(–1, 0)

 

We have,  

        

   

Let x – y + c1 = 0 and 2x + y + c2 = 0 be the lines represented by the equation (i). Then,  

     

  

Thus, the lines are x – y + 1 = 0 and 2x + y – 1 = 0  

The sides of the triangles are : 

       

Clearly, they from a right angled triangle. So, the coordinates of the orthocenter are the coordinates of the vertex forming the right angle i.e. the point of intersection of the lines

 

SIMILAR QUESTIONS

Q1

If the equation  represents two parallel straight lines, then

Q2

The gradient of one of the lines given by  is twice that of the other, then

Q3

The equation x3 + y3 = 0 represents

Q4

 

One bisector of the angle between the lines given by

 . The equation of the other bisector is

Q5

The equation  represents two mutually perpendicular lines if

Q6

The product of the perpendiculars drawn from the point (1, 2) to be the pair of lines x2 + 4xy + y2 = 0 is

Q7

The three lines whose combined equation is y3 – 4x2y = 0 form a triangle which is

Q8

 

The angle between the pair of lines whose equation is

 

Q9

 

If two of the straight lines represented by   are at right angles, then,

Q10

If the distance of a point (x1y1) from each of the two straight lines, which pass through the origin of coordinates, is δ, then the two lines are given by