The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :(A) 34(B) 34(C) 32(D) 3
Three points A,B and C taken on rectangular hyperbola xy=4 where B(−2,−2) and C(6,2/3). The normal at A is parallel to BC, then
Tangents are drawn to the hyperbola 9x2−4y2=1 parallet to the sraight line 2x−y=1. The points of contact of the tangents on the hyperbola are (A) (222,21) (B) (−229,21) (C) (33,−22) (D) (−33,22)
Let P(6,3) be a point on the hyperbola parabola a2x2−b2y2=1If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is
If a hyperbola passing through the origin has 3x−4y−1=0 and 4x−3y−6=0 as its asymptotes, then find the equation of its transvers and conjugate axes.
An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e1ande2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that e121+e221=2 .
Consider a hyperbola xy=4 and a line y=2x=4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B.
Let the given line intersects the x-axis at R. if a line through R. intersect the hyperbolas at S and T, then minimum value of RS×RT is
Tangents are drawn to the ellipse a2x2+b2y2=1 at two points whose eccentric angles are α−β and α+β The coordinates of their point of intersection are