Conic Sections — NDA Mathematics PYQs

Direction : Consider the following for the next two (02) items that follow.

The two ends of the latus rectum of a parabola are $(-2,4)$ and $(-2,-4)$.

What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?

Direction : Consider the following for the next two (02) items that follow.

The two ends of the latus rectum of a parabola are $(-2,4)$ and $(-2,-4)$.

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?