Question

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

Solution

Correct option is

x – 3 = 0 and y – 2 = 0

 

Since equation of a hyperbola and its asymptotes differ in constant terms only, 

∴ Pair of asymptotes is given by 

          

where λ is any constant such that it represents two straight lines. 

    

  

From (i), the asymptotes of given hyperbola are given by 

      

∴ Asymptotes are x – 3 = 0 and y – 2 = 0. 

SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

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

Q4

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

Q5

 

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

            

Q6

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

Q7

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

Q8

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

Q9

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

Q10

A ray emanating from the point (5, 0) is incident on the hyperbola 9x2 – 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lies in first quadrant.