Question

The slopes of the common tangents of the hyperbolas  and 

Solution

Correct option is

±1

 

Given hyperbola are  

         

and, 

         

The equation of any tangent to (i) is 

          

If it touches (ii), then 

  

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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  

Q5

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

Q6

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

Q7

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  

Q8

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 

Q9

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

Q10

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