Three normals to the parabola are drawn from the point . The area of the triangle formed by their feet on the parabola is

Answer and explanation

Correct answer: A.

**Why not the others: The value omits the factor of in calculating triangle area, while other options miscalculate the coordinates of the feet of the normals.
  1. Step 1: For parabola with , the normal at parametric point has equation .
  2. Step 2: Substitute the point : . The roots are and .
  3. Step 3: Find the coordinates of the three feet: for , ; for , ; for , .
  4. Step 4: The two non-origin vertices share , forming a vertical chord of length . The perpendicular height from to is .
  5. Step 5: Calculate triangle area: .
Answer
.

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