Question

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

Solution

Correct option is

2

 

Let e be the eccentricity of x2 – 3y2 = 1. Then,  

        

Let e1 be the eccentricity of the conjugate hyperbola. Then,     

         

            

.

SIMILAR QUESTIONS

Q1

The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola 

Q2

The equation of the chord joining two points (x1y1) and (x2y2) on the rectangular hyperbola xy = c2 is

Q3

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

Q4

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

Q5

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  

Q6

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

Q7

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

Q8

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  

Q9

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 

Q10

The slopes of the common tangents of the hyperbolas  and