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MHT CET2007MathematicsParabola

The equation to the line touching both the parabolas y²=4 x and x²=-32 y , is

Options

  1. Ax+2 y+4=0
  2. B2 x+y-4=0
  3. Cx-2 y-4=0
  4. Dx-2 y+4=0

Correct answer

D. x-2 y+4=0

Step-by-step solution

The equation of any tangent to the parabola y²=4 x is y=m x+ 1 m This touches the parabola x²=-32 y , therefore the equation x²=-32 (m x+ 1 m ) has equal roots (32 ~m )²=4 ( 32 ~m ) 8 m³=1 m= 1 2 On putting the value of m in Eq. (i), we get x-2 y+4=0

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