Question

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

Solution

Correct option is

 

Normal at  is  

        

and equation of perpendicular to (i) and passes through origin is  

        

Elimination Ï• from (i) and (ii), we will get the equation of locus of Q, as from (ii),  

                                          

 

  

    

from (i), 

          

  

SIMILAR QUESTIONS

Q1

 

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci.

 

Q2

Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity 

Q3

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

Q4

 

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

Q5

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.

Q6

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

Q7

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

Q8

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

Q9

 

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

            

Q10

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