Question

# Let S,S′ be the foci and B,B′ be the extremities of minor axis of the ellipse x216+y29=1. If a point P is selected at random inside the ellipse, then the probability that P lies inside the quadrilateral BSB′S′ is√74π √78π  √72π  √73π

Solution

## The correct option is C √72π  x216+y29=1 a=4, b=3 e=√a2−b2a2=√716=√74 ∴ Coordinates of foci are (±ae,0) S(√7,0) and S′(−√7,0) Coordinates of the ends of minor axis are (0,±b) B(0,3) and B′(0,−3) Area of the ellipse =πab=12π Area of the quadrilateral BSB′S′ =2aeb=6√7 ∴ Required probability =6√712π=√72π

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