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JEE Main201911 Jan 2019Morning ShiftMathematicsHyperbolaActual

Equation of a common tangent to the parabola y²=4 x and the hyperbola x y=2 is :

Options

  1. Ax+y+1=0
  2. Bx-2 y+4=0
  3. Cx+2 y+4=0
  4. D4 x+2 y+1=0

Correct answer

C. x+2 y+4=0

Step-by-step solution

Equation of a tangent to parabola y²=4 x is: y=m x+ 1 m This line is a tangent to x y=2 x (m x+ 1 m )=2 m x²+ 1 m x-2=0 Tangent is common for parabola and hyperbola. D= ( 1 m )²-4 m (-2)=0 1 m² +8 m=01+8 m³=0m³=- 1 8 m=- 1 2 Equation of common tangent: y=- 1 2 x-2 2 y=-x-4 x+2 y+4=0

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