The Eccentricity Of The Conjugate Hyperbola Of The Hyperbola x2 – 3y2 = 1 Is

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

The equation of the chord joining two points (x₁, y₁) and (x₂, y₂) on the rectangular hyperbola xy = c² is

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

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

PQ and RS are two perpendicular chords of the rectangular hyperbola xy= c². If C is the centre of the rectangular hyperbola, then the product of the slopes of CP, CQ, CR and CS equal to  

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

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

If e and e’ be the eccentricities of two conics S = 0 and S’ = 0 and if e² +e’² = 3, then both S and S’ can be  

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 

The slopes of the common tangents of the hyperbolas  and