Question

 

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.

 

Solution

Correct option is

 

Let two fixed point be S(ae, 0) and S’(–ae, 0). Let P(xy) be a moving point such that  

         

  

                                                                                    

     

  

Equation (i) can be re-written as 

          

From (ii) and (iii), 

        

    

  

Adding (iv) and (v), then  

          

       

  

    

 

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

 

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

Q4

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.

Q5

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

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 .