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NDA Math Conic Section
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© examsnet.com
Question : 18
Total: 34
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
[NDA II 2017]
18
π
square metres
15
π
square metres
12
π
square metres
8
π
square metres
Validate
Solution:
P
F
1
+
P
F
2
=
10
⇒
2
a
=
10
⇒
a
=
5
F
1
F
2
=
8
⇒
2
c
=
8
⇒
c
=
4
a
2
=
b
2
+
c
2
⇒
b
2
=
3
2
⇒
b
=
3
Area
=
π
a
b
=
π
×
3
×
5
=
15
π
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