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

To solve the problem, we need to prove that the locus of a point \( P(x, y) \) that moves such that the sum of its distances from the points \( (ae, 0) \) and \( (-ae, 0) \) is equal to \( 2a \) is given by the equation:

\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]

where \( b^2 = a^2(1 - e^2) \).

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