Chapter 3.3, Problem 19PSB

a

To determine

To find: The coordinates of P.

Answer to Problem 19PSB

The Coordinates of P is $\left(18,0\right)$ .

Explanation of Solution

Given information : Here, a graph is given, in which center of circle is $\left(18,10\right)$ .

According to the figure, center of the circle is at $18$ units from the y-axis and coordinate P lies on x-axis,

  $\text{⇒}x=18$ and $y=0$

  $\therefore$ Coordinates of P will be $P(18,0)$ .

b

To determine

To calculate: The area of the circle.

Area of circle is $314.28\text{ units}$ .

Given information : Here, a graph is given, in which center of circle is $\left(18,10\right)$ .

Formula used: Distance formula: $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$ and area of circle = $\pi r²$ .

Calculation: Distance from center to any point on the circle is its radius.

Here, Center = $(18,10)$ and Point P = $(18,0)$

  $\begin{array}{l}\text{⇒}d=\sqrt{{(18-18)}^2+{(0-10)}^2}\\ \text{⇒}d=\sqrt{{(0)}^2+{(-10)}^2}\\ \text{⇒}d=\sqrt{0+100}\\ \text{⇒}d=\sqrt{100}\\ \text{⇒}d=\pm 10\end{array}$

As, distance cannot be negative,

  $\text{⇒}d=10$

  $\therefore$ Radius (r) = $10$

Now, Area of circle is $\pi r²$ .

  $\begin{array}{l}\text{⇒}\frac{22}{7}\times {{\displaystyle (10)}}^2\\ \text{⇒}\frac{22}{7}\times 100\\ \text{⇒}314.28\text{ units}\end{array}$

Answer to Problem 19PSB

Area of circle is $314.28\text{ units}$ .

Explanation of Solution

Given information : Here, a graph is given, in which center of circle is $\left(18,10\right)$ .

Formula used: Distance formula: $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$ and area of circle = $\pi r²$ .

Calculation: Distance from center to any point on the circle is its radius.

Here, Center = $(18,10)$ and Point P = $(18,0)$

  $\begin{array}{l}\text{⇒}d=\sqrt{{(18-18)}^2+{(0-10)}^2}\\ \text{⇒}d=\sqrt{{(0)}^2+{(-10)}^2}\\ \text{⇒}d=\sqrt{0+100}\\ \text{⇒}d=\sqrt{100}\\ \text{⇒}d=\pm 10\end{array}$

As, distance cannot be negative,

  $\text{⇒}d=10$

  $\therefore$ Radius (r) = $10$

Now, Area of circle is $\pi r²$ .

  $\begin{array}{l}\text{⇒}\frac{22}{7}\times {{\displaystyle (10)}}^2\\ \text{⇒}\frac{22}{7}\times 100\\ \text{⇒}314.28\text{ units}\end{array}$