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Question given in the attached image . Difficulty in finding the locus of the intersecting points of the two tangents .

Question given in the attached image . Difficulty in finding the locus of the intersecting points of the two tangents .

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Grade:12th pass

1 Answers

Nicho priyatham
625 Points
8 years ago
  • equation of tangent at an eccentric angle k is
                 (x/a)cosk+(y/b)sink=0
  • equation of tangent at an eccentric angle k+900 is
                 -(x/a)sink+(y/b)cosk=0
  • solving the above equations we get point of intersection (l,m)
           l=a(cosk-sink)    ; m=b(cosk+sink)
  • on further solving we get
          2cosk=(l/a+m/b) ;  2sink=(m/b-l/a)
  •  squaring on both sides and adding we get
           (I/a)2+(m/b)2 =2
so locus of( l,m) is  option A
 PLEASE APPROVE

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