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COMEDK2012MathematicsEllipse

A man running a race-course notes that the sum of the distances from the two flag posts from him is always 10 ~m and the distance between the flag posts is 8 ~m . The equations of the path traced by the man is given by

Options

  1. Ax² 9 + y² 25 =1
  2. Bx² 9 + y² 16 =1
  3. Cx² 25 + y² 9 =1
  4. Dx² 16 + y² 25 =1

Correct answer

C. x² 25 + y² 9 =1

Step-by-step solution

Given that, S P+S^ P=10 2 a=10 a=5 and 2 a e=8a e=4b²=a² (1-e² )=a²-(a e)²=25-16=9 Hence, required equation is x² 25 + y² 9 =1

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