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JEE Main20254 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let the values of p , for which the shortest distance between the lines x+1 3 = y 4 = z 5 and r =( p i +2 j + k )+ (2 i +3 j +4 k ) is 1 6 , be a , b , (a b) . Then the length of the latus rectum of the ellipse x^2 a^2 + y^2 b^2 =1 is :-

Options

  1. A9
  2. B3 2
  3. C2 3
  4. D18

Correct answer

C. 2 3

Step-by-step solution

shortest distance = |( a - b )| ( p q ) | p q | where aligned & a =- i +0 j +0 k & ~b = p i +2 j + k & p =3 i +4 j +5 k - b =(-1- p ) i -2 j - k & q =2 i +3 j +4 k & 1 16 = |-1- p +4-1| 6 & |- p +2|=1 & p =3 & x ^2 1^2 + y ^2 3^3 =1 & ~L R = 2 a ^2 ~b = 2 1 3 = 2 3 aligned option (3)

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