Problem 1081

Find the vertex, the focus, and the directrix. Then draw the graph.

y² = -6x

Solution:-

An equation of the form y² = 4px is the standard equation of a parabola with the vertex at the origin, focus at (p,0) and directrix x = -p.

To write the equation y² = -6x in the form y² = 4px, p = – $\frac{3}{2}$

Thus , y² = -6x is equivalent to y² = 4(- $\frac{3}{2}$ )x.

The vertex is located at (0,0).

The focus is at (- $\frac{3}{2}$ ,0).

The directrix is the line x= $\frac{3}{2}$ .

The correct graph of the relation is shown to the right.