The Equations Of The Transverse And Conjugate Axes Of A Hyperbola Are Respectively 3x + 4y – 7 = 0, 4x – 3y + 8 = 0 And Their Respective Lengths Are 4 And 6. Find The Equation Of The Hyperbola.  

For what value of λ does the line y = 2x + λ touches the hyperbola  

Find the equation of the tangent to the hyperbola x² – 4y² = 36 which is perpendicular to the line x – y + 4 = 0.  

Find the equation and the length of the common tangents to hyperbola 

Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .

Find the locus of the mid-points of the chords of the hyperbola  which subtend a right angle at the origin.

Find the locus of the poles of normal chords of the hyperbola 

Find the condition for the lines Ax² + 2Hxy + By² = 0 to be conjugate diameters of  .

Find the asymptotes of the hyperbola xy – 3y – 2x = 0.

A ray emanating from the point (5, 0) is incident on the hyperbola 9x² – 16y² = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lies in first quadrant.  

A, B, C are three points on the rectangular hyperbola xy = c², find

1. The area of the triangle ABC

2. The area of the triangle formed by the tangents at A, B and C.