Question

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

Solution

Correct option is

 

Let the lines represented by 

           

  

but y = mx and y = m1x are the conjugate diameters of 

      

then, 

         

∴ From (i) and (ii), 

         

  

which is the required condition.

SIMILAR QUESTIONS

Q1

 

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

Q2

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.

Q3

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

Q4

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

Q5

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

Q6

 

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

            

Q7

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

Q8

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

Q9

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

Q10

Find the asymptotes of the hyperbola xy – 3y – 2x = 0.