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.
None of these
The equation of the required hyperbola is
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.