A parabola is given by the equation y2 = - 24x. The equation of the directrix of the parabola is. The focus of the parabola is.

see explanation

Step-by-step explanation:

The standard form of the equation of a parabola with it's principal axis along the x-axis and the vertex at the origin is

y² = 4ax (a is the distance of the directrix / focus from the vertex)

If 4a is positive the curve opens to the right. If 4a is negative the curve opens to the left.

y² = - 24x is in this form

Hence the vertex is at the origin and the curve opens to the left.

equating 4a = - 24 ⇒ a = - 6

Hence the focus is on the x-axis with coordinates ( - 6, 0)

The directrix is a vertical line 6 units to the right of the vertex with equation x = 6