Find the equation of the set of all points the sum of whose distance from the points `(3,0)a n d(9,0)` is `12.`

Explanation

`sqrt((x-3)^2+y^2)+sqrt((x-a)^2+y^2)=12`

`sqrt((x-3)^2+y^2)=12-sqrt((x-a)^2+y^2)`

Squaring both side

`(x-3)^2+y^2=144+((x-a)^2+y^2)-24sqrt((x-a)^2+y^2`

`(x-3)^2-(x-a)^2-144=-24sqrt((x-a)^2+4^2`

`12x+a-81-144=-24sqrt((x-a)^2+y^2`

`12x-72-144=-24sqrt((x-a)^2+y^2`

`(x-18)=-2sqrt((x-a)^2+y^2`

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