Question

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

Answer 1

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

which is comparable with $x^2=-4ay$, so $\left(1\right)$ represents a parabola of the standard form.

Here $4a=1\Rightarrow a=\frac{1}{4}$

$\therefore$The focus is $(0,-a)=(0,-\frac{1}{4})$ and the equation of the directrix is $y-a=0$

$\Rightarrow y-\frac{1}{4}=0$ or $4y-1=0$

The length of the latus rectum$=4a=4\times \frac{1}{4}=1$