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

Suppose that the co-ordinates of the point are (x , y), then the given condition

`sqrt([(x−ae)^2+y^2])
​+sqrt([(x+ae)^2+y^2])
​=2a .........(1) `

Now
`[(x−ae)^2+y^2]−[(x+ae)^2+y^2]=−4aex ............(2) `

`[∵(a−b)^2−(a+b)^2=−4ab] `

On dividing (2) by (1), we get

...