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AP EAMCET202123 Aug 2021Evening ShiftMathematicsParabolaActual

If the point (a, 2 a) is an interior point of the region bounded by the parabola y^2=16 x and the double ordinate through focus, then

Options

  1. Aa < 4
  2. B0 < a < 4
  3. C0 < a < 2
  4. Da>4

Correct answer

B. 0 < a < 4

Step-by-step solution

Given parabola, y^2=16 x ...(i) Comparing with y^2=4 p x Focus S=(4,0) P(a, 2 a) is in interior region of the parabola y^2-16 x=0 (2 a)^2-16 a < 0 a^2-4 a < 0 Also (a, 2 a) and vertex (0,0) are on the same side of x=4 array lr & x-4=0 So, & a-4 < 0 & a < 4 array Now, a^2-4 a < 0 0 < a < 4

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