A focal chord of the parabola has length . What is the area of the triangle formed by this chord and the lines joining its end points to the vertex of the parabola?

Answer and explanation

Correct answer: C. 40

  1. Step 1: For the parabola , the focal parameter is and the focus is . The length of a focal chord inclined at angle to the axis of symmetry is .
  2. Step 2: Solve for : . The difference between the -coordinates of the chord endpoints is .
  3. Step 3: The chord divides triangle into two sub-triangles sharing base along the axis. The total area is .
Answer
40.

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