A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 meters. The area of the path he encloses is k π then find k.

Question

A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 meters. The area of the path he encloses is k π then find k. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/4f6ab85dde120abb15c8ad7b0ae6fd20-.png" /> PS + PS S prime=10 2 a =10 a =5 2 ae =8 ae =4 e =4 / 5 b 2= a 2(1- e 2) b 2=25(1-(16/25)) b =3 A =π ab =π × 5 × 3 =15 π

Q. A man running round a race course notes that the sum of the distances of two flag-posts from him is always $10$ metres and the distance between the flag-posts is $8$ meters. The area of the path he encloses is $kπ$ then find $k$ .

$PS + PS S^{'} = 10$
$2 a = 10$
$a = 5$
$2 a e = 8$
$a e = 4$
$e = 4/5$
$b^{2} = a^{2} (1 - e^{2})$
$b^{2} = 25$ $(1 - \frac{16}{25})$
$b = 3$
$A = πab = π \times 5 \times 3$
$= 15 π$

Q. A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 meters. The area of the path he encloses is kπ then find k.

PS+PSS′=10 2a=10 a=5 2ae=8 ae=4 e=4/5 b2=a2(1−e2) b2=25(1−2516​) b=3 A=πab=π×5×3 =15π

Q. A man running round a race course notes that the sum of the distances of two flag-posts from him is always $10$ metres and the distance between the flag-posts is $8$ meters. The area of the path he encloses is $kπ$ then find $k$ .

$PS + PS S^{'} = 10$
$2 a = 10$
$a = 5$
$2 a e = 8$
$a e = 4$
$e = 4/5$
$b^{2} = a^{2} (1 - e^{2})$
$b^{2} = 25$ $(1 - \frac{16}{25})$
$b = 3$
$A = πab = π \times 5 \times 3$
$= 15 π$