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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Ellipse

JEE Main · Mathematics · Ellipse

A man running a race-course notes that the sum of the distances...

A man running a race-course notes that the sum of the distances from the two flag posts from him is always

10 \mathrm{~m}

and the distance between the flag posts is

8 \mathrm{~m}

. The equations of the path traced by the man is given by

Options

A $\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$
B $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$
C $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$
D $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$

Correct answer

C. $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$

Step-by-step solution

Given that,

S P+S^{\prime} P=10\Rightarrow \quad 2 a=10 \Rightarrow a=5

and

\quad 2 a e=8a e=4b^{2}=a^{2}\left(1-e^{2}\right)=a^{2}-(a e)^{2}=25-16=9

Hence, required equation is

\frac{x^{2}}{25}+\frac{y^{2}}{9}=

1

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