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Manipal MET2014MathematicsParabola

The common tangent of the parabolas y^2=4 x and x^2=-8 y is

Options

  1. Ay=x+2
  2. By=x-2
  3. Cy=2 x+3
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The equation of the tangent to parabola y^2=4 x is y=m x+ 1 m This is also the tangent to parabola x^2=-8 y aligned & x^2=-8 (m x+ 1 m ) & m x^2+8 m^2 x+8=0 aligned It has equal roots, if aligned & 64 m^4 &=32 m [ b^2=4 a c ] & m^3= 1 2 m= 1 [3] 2 aligned Hence, equation of the tangent is y= 1 [3] 2 x+ [3] 2 .

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