Chapter 14.1, Problem 27PSC

a.

To determine

To sketch the locus of points at a given distance.

Explanation of Solution

Given:

The point is $2$ or more units from point P and at the same time no more than $5$ or more units from point P. Point P is $(-3,4)$ .

Calculation:

The following is the sketch of the locus of thepoint which is $2$ or more units from point P and at the same time no more than $5$ or more units from point P. Point P is $(-3,4)$ -

  

b.

To determine

To describe the locus algebraically.

Answer to Problem 27PSC

  $4\le {(x+3)}^2+{(y-4)}^2\le 25$

Explanation of Solution

Given:

The point is $2$ or more units from point P and at the same time no more than $5$ or more units from point P. Point P is $(-3,4)$ .

Calculation:

The locus can be described algebraically as by the following inequality-

  $4\le {(x+3)}^2+{(y-4)}^2\le 25$

c.

To determine

To find the area of the locus.

Answer to Problem 27PSC

  $21\pi$ Square unit.

Explanation of Solution

Given:

The point is $2$ or more units from point P and at the same time no more than $5$ or more units from point P. Point P is $(-3,4)$ .

Calculation:

The area of the locus is given by-

  $\begin{array}{l}A=\pi (R^2-r^2)\\ A=\pi (25-4)\\ A=21\pi \end{array}$