Question

A hyperbola, having the transverse axis of the length , is confocal with the ellipse 3x2 + 4y2 = 12. Then, its equation is  

Solution

Correct option is

 

The equation of the ellipse is .

Let e be its eccentricity. Then, 

           .  

So, coordinates of its foci are (1, 0) and (–1, 0). 

Let the equation of the hyperbola be 

It is given that  and the hyperbola is confocal to the ellipse. 

   

    

  

Hence the equation of the parabola is    

      .

SIMILAR QUESTIONS

Q1

If the line y = 2x + λ be a tangent to the hyperbola 36x2 – 25y2 = 3600, then λ is equal to     

Q2

From any point on the hyperbola  tangents are drawn to the hyperbola . The area cut-off by the chord of contact on the asymptotes is equal to

Q3

PQ and RS are two perpendicular chords of the rectangular hyperbola xyc2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CPCQCR and CS equal to  

Q4

Let  be two points on the hyperbola . If (hk) is the point of intersection of the normal of P and Q, then k is equal to

Q5

If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is

Q6

If e and e’ be the eccentricities of two conics S = 0 and S’ = 0 and if e2 +e2 = 3, then both S and S’ can be  

Q7

If e1 is the eccentricity of the ellipse  and e2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e1e2 = 1, then the equation of the parabola, is 

Q8

The eccentricity of the conjugate hyperbola of the hyperbola x2 – 3y2 = 1 is

Q9

The slopes of the common tangents of the hyperbolas  and 

Q10

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola x2 – y2 = a2 is