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JEE Main2017MathematicsStraight LinesActual

The locus of the point of intersection of the straight lines, t x - 2 y - 3 t = 0 and x - 2 t y + 3 = 0 t ∈ R , is:

Options

  1. AA hyperbola with the length of conjugate axis 3
  2. BA hyperbola with eccentricity 5
  3. CAn ellipse with the length of major axis 6
  4. DAn ellipse with eccentricity 2 5

Correct answer

A. A hyperbola with the length of conjugate axis 3

Step-by-step solution

t x - 2 y - 3 t = 0 . . . . . . . 1 x - 2 t y + 3 = 0 . . . . . . 2 , Multiply by t and subtract from above equation, we get y 2 t 2 - 2 = 6 t Now multiply by t in first equation and subtract second, we get t 2 - 1 x = 3 t 2 - 1 ⇒ x = 3 ( t 2 + 1 ) t 2 - 1 ⇒ x 2 9 = t 2 + 1 t 2 - 1 2       &       2 y 3 = 2 t t 2 - 1 ⇒ 4 y 2 9 = 4 t 2 t 2 - 1 2 ⇒   x 2 9 - 4 y 2 9 = 1 ⇒ x 2 9 - y 2 9 4 = 1 a 2 = 9 ; ⇒ a=3 b 2 = 9 4 ⇒ b = 3 2 ∴ Le

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