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The equation to the directrix of a parabola if the two extremities of its latus rectum are (2, 4) and (6, 4) and the parabola passes through the point (8, 1) is
  • a)
    y – 5 = 0
  • b)
    y – 6 = 0
  • c)
    y – 1 = 0
  • d)
    y – 2 = 0
Correct answer is option 'B'. Can you explain this answer?
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The equation to the directrix of a parabola if the two extremities of ...
focus is (4, 4) & D can be y = 6 or y = 2

where ‘O’ is origin and S is the focus and D is directrix
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The equation to the directrix of a parabola if the two extremities of ...
The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry and passing through the focus. In this case, the line segment connecting the points (2, 4) and (6, 4) is the latus rectum. The midpoint of this line segment is the focus of the parabola.

The midpoint of the line segment with endpoints (2, 4) and (6, 4) is ((2+6)/2, (4+4)/2) = (4, 4).

Since the parabola passes through the point (8, 1), the equation of the directrix can be found by determining the line perpendicular to the axis of symmetry and passing through the point (8, 1).

The slope of the line perpendicular to the axis of symmetry is the negative reciprocal of the slope of the axis of symmetry. Since the axis of symmetry is a horizontal line (y = k), the slope of the line perpendicular to it is 0.

Therefore, the equation of the directrix is x = 8.

Answer: x = 8
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The equation to the directrix of a parabola if the two extremities of its latus rectum are (2, 4) and (6, 4) and the parabola passes through the point (8, 1) isa)y – 5 = 0b)y – 6 = 0c)y – 1 = 0d)y – 2 = 0Correct answer is option 'B'. Can you explain this answer?
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