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NDA 2 2025 Maths, question 59

Topic: Analytical geometry

Q59

Consider the following statements in respect of the equation x2+3y=0x^{2}+3y=0 :

I. The equation represents the equation to parabola that opens upwards.

II. The axis of the parabola is x=0x=0.

III. The equation of the latus rectum is 4y−3=04y-3=0.

How many of the statements given above are correct?

  1. (a) None
  2. (b) OneCorrect answer
  3. (c) Two
  4. (d) All three

Solution.

Answer: (b) One

  1. The equation is x²=−3y, so the parabola opens downward and has axis x=0.
  2. Its focus is (0,−3/4); the latus rectum lies on y=−3/4, or 4y+3=0.
  3. Only II is correct.