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JEE Main2012MathematicsParabolaActual

Statement 1 : An equation of a common tangent to the parabola y^2=16 3 x and the ellipse 2 x^2+y^2=4 is y=2 x+2 3 . Statement 2 : If the line y=m x+ 4 3 m ,(m 0) is a common tangent to the parabola y^2=16 3 x and the ellipse 2 x^2+y^2=4 , then m satisfies m^4+2 m^2=24 .

Options

  1. AStatement 1 is false, statement 2 is true
  2. BStatement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
  3. CStatement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
  4. DStatement 1 is true, statement 2 is false

Correct answer

B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Step-by-step solution

y^2=16 3 x x^2 2 + y^2 4 =1y=m x+ 4 3 m is tangent to parabola which is tangent to ellipse c^2=a^2 m^2+b^2 48 m^2 =2 m^2+4 m^4+2 m^2=24 m^2=4

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