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 dot 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^2dot Find the equation to its locus.

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

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 algebraic sum of the distances of a variable line from the points (2,0),(0,2), and (-2,-2) is zero, then the line passes through the fixed point. (a) (-1,-1) (b) (0,0) (c) (1,1) (d) (2,2)

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

A point moves so that the sum of its distances from (a e ,0)a n d(-a e ,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)dot

A point moves so that the sum of its distances from (a e ,0)a n d(-a e ,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)dot

The equation of the set of all point the sum of whose distances from the points (2, 0) and (-2, 0) is 8

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is