If the sum of the distances of a moving point from two fixed points `(ae, 0) and (-ae, 0)` be `2a`, prove that the locus of the point is: `x^2/a^2+ y^2/(a^2 (1-e^2)` =1

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a,0) is equal to a constant quantity 2c^(2). Find the equation to its locus.

Condition when donot involve a variable: ( i ) The sum of the square of the distances of a moving point from two fixed point (a;0) and (-a;0) is equal to the constant quantity 2c^(2). Find the equation to its locus?

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a,0) is equal to a constant quantity 2c^(2) Find the equation to its locus.

If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (-a, 0) is 2b^(2) , then which one of the following is correct ?

Show that the equation of the locus of a point which moves so that the sum of its distance from two given points (k, 0) and (-k, 0) is equal to 2a is : x^2/a^2 + y^2/(a^2 - k^2) =1

If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (-a,0) is 2b^(2) , then which one of the following is correct ?

A point moves so that the sum of its distances from (ae,0) and (-ae,0) is 2a, prove that the equation to its locus is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 where b^(2)=a^(2)(1-e^(2))