Question

If $(2,4)$ and $(2,-4)$ are the end points of latus rectum, then which of the following can be vertex of parabola

• A. $(0,0)$
• B. $(2,0)$
• C. $(4,0)$
• D. $(10,0)$

Answer 1

Answer: (A), (C)

$(4,0)$

Focus of the parabola will be mid point of end points of latus rectum.
$\Rightarrow$ Focus $\equiv (2,0)$

Also length of latus rectum $=8$

Hence distance of vertex from focus must be $\frac{8}{4}=2$ units and also it should be perpendicular to latus rectum.
Since latus rectum is perpendicular to $x-$ axis.

$\therefore$Vertex can be $(0,0)$ or $(4,0)$