Question

The vertex of a parabola is $(2,0)$ and its directrix is $y$ axis. The end of latusrectum in the first quadrant is

• A. $(2,4)$
• B. $(4,4)$
• C. $(6,4)$
• D. $(8,4)$

Answer 1

Answer: (B)

$(4,4)$

The length of semi latus rectum is equal to twice of distance of distance between vertex and directrix

$\Rightarrow l=2\times 2=4$

and distance of focus from vertex is equal to distance between vertex and directrix.

$\Rightarrow a=2$

Since, vertex is at $(2,0)$

Therefore, abscissa of end of latus rectum is $x_1=2+a=4$ and point of latus rectum is $(x_1,l)=(4,4)$