BITSAT 2013 Paper

Given x =

3y+k

2

... (i)
and y2 = 6x ... (ii)
⇒ y2 6 (

3y+k

2

)
⇒ y2 = 3 (3y + k) ⇒ y2 - 9y - 3k 0 ... (iii)
If line (1) touches parabola (2) then roots of quadratic equation (3) is equal
∴ (−8)2 - 4 × 1 × (-3k) ⇒ k = - 27/4