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

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

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

P is the point (-1,2), a variable line through P cuts the x & y axes at A&B respectively Q is the point on AB such that PA, PQ, PB are H.P. Find the locus of Q

AB is a chord of the circle x^(2)+y^(2)=(25)/(2).P is a point such that PA=4,PB=3. If AB=5 , then distance of P from origin can be:

A variable line through point P(2,1) meets the axes at A and B. Find the locus of the circumcenter of triangle OAB (where O is the origin.

A variable line through the point P(2,1) meets the axes at A and B .Find the locus of the centroid of triangle OAB (where O is the origin).

If secants are drawn thro P(2 -1) to the circle x^(2)+y^(2)+2x=0 meeting it at A&B and Q lies on segment AB then locus of Q such that PA, PQ ,PB are in H.P is ax+by+c=0{a b c are least possible integers } then |a+b+c|=

A variable point P is on the circle x^(2)+y^(2)=1 on xy plane.From point P, perpendicular PN is drawn to the line x=y=z then the minimum length of PN is:

A circle passes through the point (3,4) and cuts the circle x^(2)+y^(2)=c^(2) orthogonally,the locus of its centre is a straight line.If the distance of this straight line from the origin is 25. then a^(2)=