A(a,0) and B(-a,0) are two fixed points, find the locus of a point P which moves such that 3|PA| = 2|PB|.

If A(-2,2,3)a n dB(13 ,-3,13) are two points. Find the locus of a point P which moves in such a way that 3P A=2P Bdot

If P(1,0) ,Q(-1,0) and R(2,0) are three given points ,then the locus of point S satisfying the relation (SQ)^(2)+(SR)^(2)=2(SP)^(2) is

Statement I Let A-= (0,1) and B -= (2,0) and P be a point on the line 4x+3y+9=0 then the co - ordinates of P such that |PA -PB| is maximum is (-12/5,17/5) Statement II |PA - PB | le |AB|

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

If A and B be the points (3, 4, 5) and (-1,3, -7), respectively, find the equation of the set of points P such that PA^2 + PB^2 = k^2 , where k is a constant.

Let A=(-3, 4) and B=(2, -1) be two fixed points. A point C moves such that tan((1)/(2)angleABC):tan((1)/(2)angleBAC)=3:1 Thus, locus of C is a hyperbola, distance between whose foci is

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a . Let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.

If A and B be the points (3,4,5) and (-1,3,-7) respectively, find the equation of the set of point P such that PA^2+PB^2=k^2 , where k is constant.

If A and B are the points (3, 4, 5) and (-1, 3,-7) respectively then theset of points Psuch that PA ^(2) + PB ^(2) = K ^(2), where K is a constant lie on a proper sphere if:

The ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.