A) 12 units
B) 13 units
C) \[\sqrt{149}\] units
D) \[\sqrt{49}\] units
Correct Answer: C
Solution :
Since, circle is concentric to the ellipse and passes through the foci \[{{S}_{1}}\] and \[{{S}_{2}}\]. Hece, \[{{S}_{1}}{{S}_{2}}\] in the diameter of the circle. Then, area of \[\Delta P{{S}_{1}}{{S}_{2}}\] \[=\frac{1}{2}\,({{S}_{1}}P)\,({{S}_{2}}P)\] as \[{{S}_{1}}{{S}_{2}}\] is daimeter But, \[{{S}_{1}}P+{{S}_{2}}P=2a=17,\] then Area \[=\frac{1}{2}\,x\,(17-x)\,=35,\] where \[{{S}_{1}}P=x\] \[\Rightarrow \] \[{{x}^{2}}-17x+70=0\] \[\Rightarrow \] \[x=7,\,\,10\] \[\therefore \] \[{{S}_{1}}{{S}_{2}}\,\sqrt{PS_{1}^{2}+PS_{2}^{2}}\] \[=\sqrt{49+100}\] \[=\sqrt{149}\] unitsYou need to login to perform this action.
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