Question

What is the radius for the circle given by the equation x^2+(y -3)^2 = 21

Round your answer to the nearest thousandth._______

Answer 1

`\bf\textit{equation of a circle}\\\\(x- h)^2+(y- k)^2= r^2\qquadcenter~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquadradius=\stackrel{}{ r}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\x^2+(y-3)^2=21\implies (x-0)^2+(y-3)^2=(√(21))^2\qquad \begin{cases}center~(0,3)\\r=√(21)\end{cases}\\\\\\r\approx 4.58257569495584000659\implies r = \stackrel{\textit{rounded up}}{4.583}`

Answer 2

4.583

Explanation:

The equation for the radius r of a circle can be found from

(x – h)2 + (y – k)2 = r2,

Where h and k are the center points along the x and y axis respectively.

Comparing with the equation given;

x^2+(y -3)^2 = 21

h = 0, y = 3 and r^2 = 21

r = √21

= 4.583 (to the nearest thousand)

Note that unit of measurement may apply where given.