Question

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

Solution

Correct option is

 

The given ellipse is  

          

Comparing with   

          

      

  

                                   

∴ Foci of ellipse are (±ae, 0) i.e., (±4, 0)  

So, the coordinates of foci of the hyperbola are (±4, 0)   

Let e’ be the eccentricity of the required hyperbola and its equation be  

              

The coordinates of foci are (±Ae’, 0)  

  

  

.  

  

                  

Substituting the value of A and B in (i), we get  

             

     

which is required hyperbola.

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

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

Q7

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

Q8

 

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

            

Q9

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

Q10

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