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AP EAMCET202022 Sep 2020Evening ShiftMathematicsParabolaActual

The largest value of k for which the circle x^2+y^2=k^2 lies completely in the interior of the parabola y^2=4 x+16 is

Options

  1. A4 3
  2. B2 3
  3. C2 6
  4. D4 6

Correct answer

B. 2 3

Step-by-step solution

Given, parabola is y^2=4 x+16 y^2=4(x+4) Let parametric point on parabola be (t^2-4,2 t ) distance O P k array rlrl & & (t^2-4 )^2+4 t^2 & k^2 t^4+16-8 t^2+4 t^2 & k^2 & & t^4-4 t^2+16-k^2 & 0 & & D & 0 & & 16-4 (16-k^2 ) & 0 & & 4-16+k^2 & 0 k^2 12 k & [-2 3 , 2 3 ] array Hence, option (2) is correct.

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