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

1.	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`
Answer» 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` Putting h=x,k=y `x^2/a^2+y^2/b^2=1`.

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`
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