Q194 / 270 · NDA 2021 (Phase 2) · Mathematics

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?

  • A
    Only one
  • Correct answer
    B
    Two
  • C
    Four
  • D
    Infinite

Solution

$\text { Focus }=\left(\frac{-2-2}{2}, \frac{4-4}{2}\right)=(-2,0)$ Length of lectus rectum: $\begin{aligned} & =|4 a|=\left|\sqrt{(-2+2)^2+(4+4)^2}\right|=8 \\ & \Rightarrow a= \pm 2 \end{aligned}$ So, there are two parabola can be drawn.

Hence, the correct answer is option: 'B'.

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