Describe the locus of a point P, so that :
`AB^(2)=AP^(2)+BP^(2)`,
where A and B are two fixed points.

Find the locus of point P if AP^2-BP^2=18 where A-=(1,2,-3) and B-=(3,-2,1).

Find the locus of the point P such that PA^2+PB^2=2c^2 :where A(a,0),B(-a,0) and 0 lt |a| lt |c|.

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point P .

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

Find the locus of a variable point (at^2, 2at) where t is the parameter.

A(2, 0) and B(4, 0) are two given points. A point P moves so that PA^(2)+PB^(2)=10 . Find the locus of P.

If the equal sides AB and AC each of whose length is a of a righ aisosceles triangle ABC be produced to P and so that BP. CQ=AB^2, the line PQ always passes through the fixed point

A variable line L passing through the point B(2, 5) intersects the lines 2x^2 - 5xy+2y^2 = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression.