Question

All chords of the curve  which subtend a right angle at the origin always pass through the point

Solution

Correct option is

(1, –2)

 

Let ax + by = 1 be a family of chords of the curve

  subtending a right angle at the origin.   

The combined equation of the straight lines joining the origin to the points of intersection of  and the chord ax + by =1 is  

          

This represents a pair of perpendicular lines.   

  

     

   

 

SIMILAR QUESTIONS

Q1

 

If one of the lines represented by the equation   is a bisector of the angle between the linesxy = 0, then λ =

Q2

If θ is the angle between the straight lines given by the equation , then cosec2 θ =

Q3

 

The line y = mx bisects the angle between the lines

 , if

Q4

 

If two pairs of straight lines having equations   have one line common then a =

Q5

The point of intersection of the The Pair of Straight Lines given by 

Q6

 

The square of the distance between the origin and the point of intersection of the lines given by  

           

Q7

The centroid of the triangle whose three sides are given by the combined equation  

Q8

If first degree terms and constant term are to be removed from the equation , then the origin must be shifted at the point

Q9

The angle between the straight lines joining the origin to the points of intersection of  and 3x – 2y = 1 is

Q10

 

If the pair of lines represented by   intersect on y-axis, then