Question

Find the coordinates of the focus and the vertex, the equations of the directrix, the axis, and length of latus rectum of the parabola $x^2=-16y.$

Answer 1

The given equation is of the form $x^2=-4ay,$ where $4a=16,$ i.e., $a=4.$

So, it is a case of downward parabola.

Its focus is $F(0,-a),$ i.e. $F(0,-4).$

Its vertex is $O(0,0).$

The equation of the directrix is $y=a,$ i.e., $y=4.$

Its axis is y-axis, whose equation is $x=0.$

Length of latus rectum = $4a=(4\times 4)$ units = 16 units.