Parabola · Mathematics · NDA

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?

In the parabola $y^2 = 8x$, the focal distance of a point P lying on it is 8 units. Which of the following statements is/are correct?

1. The coordinates of $P$ can be $\left(6, 4\sqrt{3}\right)$.

2. The perpendicular distance of $P$ from the directrix of parabola is 8 units.

Select the correct answer using the code given below:

Consider the following statements in respect of such parabolas:

1. One of the parabolas passes through the origin (0, 0).

2. The focus of one of the parabolas lies at (-2, 0).

Which of the above statements is/are correct?