Find The Locus Of The Mid-points Of The Chords Of The Hyperbola  which Subtend A Right Angle At The Origin.

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Question

Find the locus of the mid-points of the chords of the hyperbola  which subtend a right angle at the origin.

Solution

Correct option is

 

Let (hk) be the mid-point of the chord of the hyperbola. Then its equation is   

            

    

The equation of the lines joining the origin to the points of intersection of the hyperbola and the chord (i) is obtained by making homogeneous hyperbola with the help of (i) 

  

                                                

The lines represented by (ii) will be at right angle if   

     Coefficient of x2 + Coefficient of y2 = 0 

  

  

Hence, the locus of (hk) is  

        .

 

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Q9

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Q10

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