Consider the following statements in respect of the equation x^{2}+3y=0 : I. The equation represents the equation to parabola that opens upwards. II. The axis of the parabola is x=0. III. The equation of the latus rectum is 4y-3=0. How many of the statements given above are correct?

Explanation

The equation x^2 = -3y represents a parabola opening downwards, not upwards (Statement I is false). Its axis is x=0 (Statement II is true). Comparing with x^2 = -4ay, we have 4a = 3, so a = 3/4. The latus rectum is y = -a = -3/4, which gives 4y + 3 = 0, not 4y - 3 = 0 (Statement III is false). Thus, exactly one statement is correct.

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