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

A variable straight line through A(-1,-1) is drawn to cut the circle x^(2)+y^(2)=1 at the point B and C.P is chosen on the line ABC, If AB,AP,AC are in A.P. then the locus of P is

A variable line through A(6,8) meets the circle x^(2)+y^(2)=2 at B and C.P is a point on BC such that AB,AP AC are in H.P.Then the minimum distance of the origin from locus of P is

If a,b,c are in G.P and a,p,q are in A.P such that 2a, b+p, c +q are in G.P ., then the common difference of A.P is

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If these tangents cut the coordinates axes at 4 concyclic points, then the locus of P is

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. If the tangent to the curve C cuts the corrdinate axes at A and B, then the locus of the middle point of AB is

If the sum of the slopes of the normals from a point P to the hyperbola xy=c ^(2) is constant k (k gt 0), then the locus of point P is