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Chapter 1: Q 9. (page 50)

Find the center and radius of the circle. Write the standard form of the equation.

Short Answer

Expert verified

Center is $(\frac{5}{2}, 2)$ .

Radius is $\frac{3}{2}$ units.

Standard form of the equation is ${(x - \frac{5}{2})}^{2} + (y - 2)^{2} = \frac{9}{4}$ .

Step by step solution

01

Step 1. Given information

Figure of a circle is as follows:

02

Step 2. Find the center and radius of a circle.

Diameter is the distance between the points $(1, 2)$ and $(4, 2)$

Diameter $= \sqrt{(4 - 1)^{2} + (2 - 2)^{2}}$

$= \sqrt{9 + 0} = 3$

$\begin{array}{rcl} Radius & = & \frac{Diameter}{2} \\ = & \frac{3}{2} \end{array}$

Center is the midpoint of the points $(1, 2)$ and $(4, 2)$

$\begin{array}{rcl} Center & = & (\frac{1 + 4}{2}, \frac{2 + 2}{2}) \\ = & (\frac{5}{2}, 2) \end{array}$

03

Step 3. Find the standard form of the equation of a circle.

Equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^{2} + (y - k)^{2} = r^{2}$ .

Therefore, equation of the circle with center $(\frac{5}{2}, 2)$ and radius $\frac{3}{2}$ is

role="math" localid="1646125761348" $\begin{array}{rcl} {(x - \frac{5}{2})}^{2} + (y - 2)^{2} & = & {(\frac{3}{2})}^{2} \\ {(x - \frac{5}{2})}^{2} + (y - 2)^{2} & = & \frac{9}{4} \end{array}$

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Most popular questions from this chapter

If $(x, y)$ are the coordinates of a point P in the xy-plane, then x is called the ________ of P and y is the ________ of P.

The coordinate axes divide the xy-plane into four sections called _________.

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends \(40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends \)60,000, then 200,000 boxes will be sold.

(a) Write a linear equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

(b) How much advertising is needed to sell 300,000 boxes of cereal?

(c) Interpret the slope.

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Tell whether the given points are on the graph of the equation.

$Equation : y = x^{4} - \sqrt{x} Points : (0, 0); (1, 1); (- 1, 0)$

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