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BITSAT2023MathematicsParabolaActual

The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is

Options

  1. Ay=4(x-2)
  2. By=4(x-1)
  3. Cy=4(x+1)
  4. Dy=4(x+2)

Correct answer

B. y=4(x-1)

Step-by-step solution

Equation of tangent of parabola y=x^2 be t x=y+a t^2 ...(i) y=t x- t^2 4 Solve with y =-( x -2)^2 t x- t^2 4 =-(x-2)^2 x^2+x(t-4)- t^2 4 +4=0 Here, Discriminant =0 . (t-4)^2-4 (4- t^2 4 )=0 t^2-4 t=0 t=0 or t =4 Put value of t in eq. (i), then y=4(x-1) .

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