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NDA 2 2024 Maths, question 60

Topic: Analytical geometry

Q60

Consider the points P(4k,4k)P(4k,4k) and Q(4k,−4k)Q(4k,-4k) lying on the parabola y2=4kxy^{2}=4kx. If the vertex is AA, then what is ∠PAQ\angle PAQ equal to?

  1. (a) 60∘60^{\circ}
  2. (b) 90∘90^{\circ}Correct answer
  3. (c) 120∘120^{\circ}
  4. (d) 135∘135^{\circ}

Solution.

Answer: (b) 90∘90^{\circ}

  1. The vertex is A=(0,0).
  2. The dot product AP·AQ=(4k)²−(4k)²=0, so the two nonzero rays are perpendicular and ∠PAQ=90°.
  3. As the curve is a parabola, k≠0 is implicit; k=0 would make the angle undefined.