Find locus of point P such that `PF_1+PF_2=2a` and `F_1-=(c,0)` & `F_2-=(-c,0)`

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

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|.

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|.

Find the locus of the point P, sum of whose distance from the points F_1(2,0) and F_2(-2,0) is constant and equal to 6.

Let A(1,0), B(-1,0), C(2, 0) then the locus of a point P such that PB^(2)+ PC^(2) = 2PA^(2) is

Find the locus of the point P, sum of whose distances from the points F_1(-2,1) and F_2(-5,5) is a constant equal to 5.

Let F_(1),F_(2) are the foci of the ellipse 4x^(2)+9y^(2)=36 and P is a point on ellipse such that PF_(1)=2PF_(2), then the area of triangle PF_(1)F_(2) is

If P(x ,y) is any point on the ellipse 16 x^2+25 y^2=400 and F_1=(3,0)F_2=(-3,0) , then find the value of P F_1+P F_2dot