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If the locus of the moving poin P(x,y) s...

If the locus of the moving poin P(x,y) satisfying `sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a` is an ellipse, then find the values of a.

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The correct Answer is:
`agt4`
We have `underset("distance between" P(x,y) and S (1,0))(sqrt((x-1)^(2)+y^(2)))+underset("distance between"P(x,y)and S' (-1sqrt(12)))sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a`
`:. SP+S'P=a`
So, licus of P is ellipse if
`agtSS'`
or `agtsqrt(4+12)`
or `agt4`
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