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Chapter 10: Q 10. (page 643)

Answer Problem using the figure.

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

Short Answer

Expert verified

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

y = -2.

Step by step solution

01

Step 1. Given information.

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

02

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.

03

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.

04

Step 4. Conclusion.

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

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