Question

Answer Problem using the figure.

If a = 4, then the equation of the directrix is______ .

Short answer

If a = 4, then the equation of the directrix is

y = -2.

Step-by-step solution

Step 1. Given information.

We have given a = 4 and graph of parabola is,

Step 2. Concept used.

Directrix of the parabola:

The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

Formula for the directrix for upward parabola is: y = k - a.

Step 3. Explanation.

We have given graph is,

This parabola is upward parabola so directrix of the parabola is,

$y=k-a$.

Where " k " is the y-coordinate of the vertex.

From figure we have vertex = (3, 2).

So equation for the directrix is,

y = 2 - 4 = -2.

Step 4. Conclusion.

If a = 4, then the equation of the directrix is y = -2.