Question

What is the center and the radius of the the circle(x + 4)2 + (y + 6)2 = 64? center (-4, -6), radius = 64 center (-4,-6), radius = 8 center (4,6), radius = 8 center (4,6). radius = 64

Answer 1

Step 1: Problem

What is the center and the radius of the the circle(x + 4)2 + (y + 6)2 = 64?

Step 2: Concept

`\begin{gathered} \text{General equation of a circle } \\ (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ r\text{ = radius} \\ (\text{ a, b) is the center} \end{gathered}`

Step 3: Method

`\begin{gathered} (x+4)^2+(y+6)^2\text{ = 64} \\ (x+4)^2+(y+6)^2=8^2 \\ \text{Next } \\ \text{Compare ( x + 4 )}^2+(y+6)^2=8^2with(x-a)^2+(y-b)^2=r^2 \\ \text{ a = -4 } \\ b\text{ = - 6} \\ r\text{ = 8} \end{gathered}`

Step 4: Final answer

Center = ( a, b ) = ( -4, -6 )

Radius r = 8

center ( - 4, - 6 ) , radius = 8