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`

Explanation

AP+BP=2h

`AP=sqrt((h-he)^2+k^2)`

`BP=sqrt((h+he)^2+k^2`

`AP+BP=2h`

`(AP+BP)^2=4a^2`

`AP^2+BP^2+2(AP)(BP)=4a^2`

`(h-ae)^2+k^2+(h+ae)^2+k^2+2sqrt(((h-ae)^2+k^2)(h+ae)^2+k^2`

`h^2/a^2+k^2/b^2=1`

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