Consider a straight line `x/a + y/b =1` , such that it cuts the asymptotes of hyperbola `xy = 1` in points A and B and the hyperbola itself in P and Q, then`(AP )/ (BQ) =lamda` lambda where `2lambda + 1` is

A transvers axis cuts the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at P and P' and the asymptotes at Q and Q'. Prove that PQ=P'Q' and PQ'=P'Q.

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. Shortest distance between the line and hyperbola is

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. Shortest distance between the line and hyperbola is

From a point A a varible straight line is drawn to cut the hyperbola xy=c^2 at B and C. If a point P is chosen on BC such that AB,AP,AC are in G.P., then the locus of P is

The locus of the point of intersection of lines (x)/(a)+(y)/(b)=lambda and (x)/(a)-(y)/(b)=(1)/(lambda), where lambda is a parameter, is

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. Locus of circumcentre of triangle OAB is