Chapter 9.2, Problem 36PPS

a.

To determine

To make a line that is perpendicular to the sides of sheet and mark a point about midway between the sides of the sheet.

Explanation of Solution

Given:

The following is the sheet of paper that is about $15$ inches long and $12$ inches wide.

  

Calculation:

The focus is at $(2,6)$ , Directrix is at $x=1$ , Vertex at $\left(\frac{1+2}{2},6\right)=(1.5,6)=(h,k)$

  

b.

To determine

To form another outline of a parabola.

Explanation of Solution

Given:

The focus is about $3$ inches from the directrix.

Calculation:

The focus is at $(4,6)$ , Directrix is at $x=1$ , Vertex at $\left(\frac{1+4}{2},6\right)=(2.5,6)=(h,k)$

  

c.

To determine

To form third outline of a parabola.

Explanation of Solution

Given:

The focus is about $5$ inches from the directrix.

Calculation:

The focus is at $(6,6)$ , Directrix is at $x=1$ , Vertex at $\left(\frac{1+6}{2},6\right)=(3.5,6)=(h,k)$

  

d.

To determine

To compare the shapes of three parabolas and find out how does the distance between the focus and the directrix affect the shape of parabola.

Explanation of Solution

As the distance between the focus and the directrix increases, the parabola widens more since a gets smaller. When the distance decreases the arms come closer.