Question

Find the equation of directrix and length of latus rectum of the parabola $x^2=16y$.

• A. $y-4=0$ and $16$
• B. $y+4=0$ and $16$
• C. $y-4=0$ and $4$
• D. $y+4=0$ and $4$

Answer 1

Answer: (B)

$y+4=0$ and $16$

Given equation of parabola

$x^2=16y$

general form of parabola is

$(x-h{)}^2=4a(y-k)$

here $(h,k)=(0,0)$

and $a=4$

focus lies at (0,4) since $a=4$

dirctrix passes through focus so equation of directrix is $y+4=0$

length of latus rectum is 4a

so $4\left(4\right)=16$

therefore length of latus rectum is $16$