The slope of the line touching both the parabolas

The slope of the line touching both the parabolas y2 = 4x and x2 = -32y is

  1. 1/2
  2. 2/3
  3. 3/2
  4. 1/8

Answer

Equation of the tangent at A(t2, 2t)

yt = x + t2 is tangent to x2 + 32y = 0 at B

x2 + 32(x/t + t) = 0

x2 + 32x/t + 32t = 0

(32/t)2 - 4(32t) = 0

32(32/t2 - 4t) = 0

The correct option is A.