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

The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is 

The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latusrectum 4, is given by

The equation of the tangent to the curve 4x² – 9y² = 1 which is parallel to 4y = 5x + 7, is

The equation of the tangent parallel to y = x drawn to  is

If m is a variable, the locus of the point of intersection of the lines  is a/an 

If the chords of contact of tangents from two points (x₁, y₁) and (x₂, y₂) to the hyperbola  are at right angles, then  is equal to 

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     

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