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KCET2009MathematicsParabola

For the parabola y ²=4 x , the point P whose focal distance is 17 , is

Options

  1. A(8,8) or (8,-8)
  2. B(4,8) or (4,-8)
  3. C(2,8) or (2,-8)
  4. D(16,8) or (16,-8)

Correct answer

D. (16,8) or (16,-8)

Step-by-step solution

Given, y ²=4 x Let P ( h , k ) be any point on the parabola ( h -1)²+( k -0)²=17² Also, k ²=4 ~h h ²+1-2 ~h +4 ~h =289 h ²+2 ~h -288=0 ( h +18)( h -16)=0 h =16 ( h cannot be negative ) k ²=64 k = 8 Points are (16,8) or (16,-8) .

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