Question

Find the locus of the poles of normal chords of the hyperbola 

Solution

Correct option is

 

Let (x1y1) be the pole of a normal chord   

          

of  the hyperbola

          

then (i) must be identical with the polar of (x1y1) with respect to    

  

Comparing (i) and (iii), we obtained

        

   

     

  

  

  

∴ The required locus of (x1y1) is 

       .

SIMILAR QUESTIONS

Q1

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Q2

 

Find the equation of the hyperbola whose foci are (6, 4) and (–4, 4) and eccentricity is 2.

Q3

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distances of one of its vertices from the foci are 9 and 1 units.

Q4

The foci of a hyperbola coincide with the foci of the ellipse . Find the equation of the hyperbola if its eccentricity is 2.

Q5

For what value of λ does the line y = 2x + λ touches the hyperbola  

Q6

Find the equation of the tangent to the hyperbola x2 – 4y2 = 36 which is perpendicular to the line x – y + 4 = 0.  

Q7

 

Find the equation and the length of the common tangents to hyperbola 

            

Q8

Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .

Q9

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

Q10

Find the condition for the lines Ax2 + 2Hxy + By2 = 0 to be conjugate diameters of  .