Question

Find the focus and equation of the latus rectum if x^2+ky=0, where k>0

Answer 1

Comparing the given equation $x^2=-ky$ of parabola with standard equation $x^2=-4ay$ , we obtain $k=4a$

$\implies a = k/4$

Focus of standard parabola is $(0,-a)$

So, for the given parabola, focus is $(0,-\frac{k}{4})$

Equation of latus rectum is given by $y=-a$

Hence for the given parabola, equation of latus rectum is, $y=-\frac{k}{4}$