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In the adjacent figure, a parabola is drawn to pass through the vertices B , C and D of the square A B C D . If A ( 2 , 1 ) ,   C ( 2 , 3 ) , then the focus of this parabola is:

Options

  1. A1 , 11 4
  2. B2 , 11 4
  3. C3 , 13 4
  4. D2 , 13 4

Correct answer

B. 2 , 11 4

Step-by-step solution

We observe that x -coordinate of A and C is same. Hence, the diagonal A C is parallel to y -axis and its mid-point is ( 2 , 2 ) . Now, other diagonal will be parallel to x -axis as given quadrilateral is square. Thus, B ≡ ( 3 , 2 ) and D ≡ ( 1 , 2 ) . Now, equation of parabola can be assumed as : x - 2 2 = λ y - 3 Since it passes through B 3 ,   2 , so 1 = - λ ⇒ λ = - 1 ∴ x - 2 2 = - y - 3 Hence, axis is x - 2 = 0 . y -coordinate of focus is y - 3 = - 1 4 ∴ Focus &#

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