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AP EAMCET202422 May 2024Evening ShiftMathematicsParabolaActual

Equation of the line touching both parabolas y^2=4 x and x^2=-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

y^2=4 x ...(i) Equation of tangent of (i) is, y=m x+ 1 m , ...(ii) Also, x^2=-32 y ...(iii) Equation of tangent of (iii) is y=m x-(-8 m)^2 y=m x+8 m^2 ...(iv) From (ii) and (iv), 1 m =8 m^2 m= 1 2 So, from (ii), y= x 2 +2 x-2 y+4=0 .

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