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NDA 2 2024 Maths, question 88

Topic: Integral calculus

Passage · Q87 to Q88

The area bounded by the parabola y2=kxy^{2}=kx and the line x=kx=k, where k>0k>0, is 4/3 square units4/3\text{ square units}.

Q88

What is the area of the parabola bounded by the latus rectum?

  1. (a) 1/6 square unit1/6\text{ square unit}Correct answer
  2. (b) 2/3 square unit2/3\text{ square unit}
  3. (c) 1 square unit1\text{ square unit}
  4. (d) 4/3 square units4/3\text{ square units}

Solution.

Answer: (a) 1/6 square unit1/6\text{ square unit}

  1. With k=1 the parabola is y²=x, so 4a=1 and the latus rectum is x=1/4 with endpoints y=±1/2.
  2. The enclosed area is ∫ from −1/2 to 1/2 of (1/4−y²)dy=1/6 square unit.