A) 8
B) 6
C) 10
D) 12
Correct Answer: C
Solution :
[c] The ellipse can be written as, \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] Here \[{{a}^{2}}=25,{{b}^{2}}=16,\] but \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\Rightarrow 16/25\]\[=1-{{e}^{2}}\] \[\Rightarrow {{e}^{2}}=1-16/25=9/25\Rightarrow e=3/5\] Foci of the ellipse are \[(\pm ae,0)=(\pm 3,0),\] i.e., \[{{F}_{1}}\] and \[{{F}_{2}}\] \[\therefore \] We have \[P{{F}_{1}}+P{{F}_{2}}=2a=10\] for every point P on the ellipse.
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