The equation of the line passing through the centre of a rectangular hyperabola is x – y – 1 = 0. If one of its asymptotes is 3x – 4y – 6 = 0, the equation of the other asymptotes is


Correct option is

4x + 3y + 17 = 0


The point of intersection of the line x – y – 1 = 0, which passes through the centre of the hyperbola, and the asymptotes 3x – 4y – 6 = 0 is the centre of the hyperbola. So, its coordinates are (–2, –3). Since asymptotes of a rectangular hyperbola are always at right angle. So, required asymptote is perpendicular to the given asymptote and passes through the centre (–2, –3) of the hyperbola and hence is equation is  




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


The slopes of the common tangents of the hyperbolas  and 


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


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


If a hyperbola passing through the origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes, then the equations of its transverse and conjugate axes are  


If H(xy) = 0 represents the equation of a hyperbola and A(xy) = 0, C(x,y) = 0 the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point (α, β) in the plane,  are in


The equation of a tangent to the hyperbola  which make an angle π/4 with the transverse axis, is


For the hyperbola  which of the following remains constant with change in ‘α’


If radii of director circles of  are 2r and rrespectively and ee and eh be the eccentricities of the ellipse and hyperbola respectively, then