Question

Find the coordinates of focus,the axis, the equation of the directrix and the length of the latus-rectum of the parabola represented by the equation $y^2=16x$

Answer 1

The given equation is $y^2=16x$ .......$\left(1\right)$

which is same as $y^2=4ax$, so $\left(1\right)$ represents standard parabola,and its axis lies along the $x-$axis.Hence $x-$axis itself is the axis of the given parabola.

Also,$4a=16\Rightarrow a=\frac{16}{4}=4$

$\therefore$ focus is $(a,0)=(4,0)$ and the equation of the directrix is $x+a=0$

$x+4=0$

Length of the latus rectum$=4a=4\times 4=16$