Question

For parabola $y^2=84x$, end points of latus rectum and length of L.R. is

• A. $(0,21),84$
• B. $(21,\pm 42),84$
• C. $(0,\pm 21),42$
• D. $(\pm 21,42),21$

Answer 1

Answer: (B)

$(21,\pm 42),84$

For the parabola $(y-k{)}^2=4a(x-h)$,

end points of latus rectum are $(h+a,k+2a)$ and $(h+a,k-2a)$

and length of latus rectum $=4a$

For the given parabola $y^2=84x=4\left(21\right)x$

$h=k=0$ and $a=21$

So, end points of latus rectum are $(21,42)$ and $(21,-42)$

and length of latus rectum $=84$

So, the answer is option (B).