A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m . The area of the path he encloses is

Step-by-step solution

Given that sum of the distances of two flag-posts from him is always 10 m . So, the race course is in the shape of ellipse. From the given figure, Mf ₁+ Mf ₂=10 Let ' a ' be the length of semi major axis and 'b' be the length of semi minor axis. aligned & Mf ₁+ Mf ₂=10 2 a =10 a =5 & Also, f ₁ f ₂=8 & Let f ₁=( C , 0) and f ₂=(- C , 0) aligned f ₁ f ₂=8 2 C =8 C =4 We know, a ^2= b ^2+ c ^2 5^2= b ^2+4^2 aligned & b ^2=25-16=9=3^2 & ~b =3 . aligned