Chapter 1.4, Problem 21AYU

To determine

To find:

1. The centre $\left(h,k\right)$ and radius of the circle $x²+y²=4$

2. The graph of the circle

3. Intercepts of the circle, if any

Answer to Problem 21AYU

$\text{Centre }\left(0,0\right);\text{ radius }=2;$

$x\text{-intercepts }=\pm 2;y\text{-intercepts }=\pm 2$

Explanation of Solution

Given:

Equation of the circle $x²+y²=4$

Calculation:-

Let us write the equation of the circle in standard form $\left(x-0\right)²+(y-0)²=\left(2\right)²$.

Compare this equation with the equation $\left(x-h\right)²+(y-k)²=\left(r\right)²$.

The comparison yields the information about the circle. We see that $h=0,k=0$ and $r=2$.

The circle has centre $\left(0,0\right)$ and a radius 2 units. To graph the circle, first plot the centre $\left(0,0\right)$. Since the radius is 2 units, locate four points on the circle by plotting 2 units to the left, to the right, up and down from the centre. These four points can be used to sketch the graph.

To find the $x\text{-intercepts}$, if any, let $y=0$ and solve for $x$.

$x²+0²=4$

$x²=4$

$x=\pm 2$

$x\text{-intercepts}$ are 2 and $-2$.

To find the $y\text{-intercepts}$, if any, let $x=0$ and solve for $y$.

$\left(0\right)²+y²=4$

$y²=4$

$y=\pm 2$

$y\text{-intercepts}$ are 2 and $-2$.