The foci of a hyperbola are (–5, 18) and (10, 20) and it touches the y-axis. The length of its transverse axis is


Correct option is


Let 2a and 2b be respectively lengths of transverse and conjugate axes of the hyperbola and eccentricity be e


       2ae = Distance between foci    



We know that the product of lengths of perpendicular from two foci on any tangent to a hyperbola is b2. Since given hyperbola touches y-axis i.e.x = 0. 



Hence, length of transverse axis, 




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’


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


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


 are two points on the hyperbola  such that  (a constant), then PQ touches the hyperbola 


The product of the lengths of perpendicular drawn from any point on the hyperbola x2 – 2y2 – 2 = 0 to its asymptotes is


If tangent to any members of family of hyperbolas  is not a normal to any member of family of circles , where μ is any real parameter, then θbelongs to