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If A (3, 0), B (–3, 0) and PA + PB = 10, then the equation of the locus of P is

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$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$

$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$

$\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$

$\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$

answer is A.

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Detailed Solution

$A (3, 0), B (- 3, 0), P A + P B = 10 \Rightarrow \frac{4 (x - 0)^{2}}{100} + \frac{4 (y - 0)^{2}}{100 - 36} = 1 \Rightarrow \frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$

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