First slide

Ellipse

Question

A man running a race course notes that the sum of distance of two flag posts from him is always 10 meters and distance between the flag post’s is 8 meters and Locus of man is a conic then length of the latus rectum of the conic is _______

Moderate

A

$\frac{12}{5}$
B

$\frac{3}{5}$
C

$\frac{4}{5}$
D

$\frac{18}{5}$

Solution

$Given SP + S^{1} P = 2 a \Rightarrow 2 a = 10 \Rightarrow a = 5; 2 a e = 8 \Rightarrow e = \frac{4}{5} \Rightarrow b = 3;$
$Latus rectum = \frac{2 b^{2}}{a} = \frac{18}{5}$

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