Question

Circles on a coordinate plane

Answer 1

Given: The center and radius of a circle

`\begin{gathered} center=(h,k) \\ radius=r \end{gathered}`

To Determine: The equation of the circle

1) Circle A centered at the origin with radius 6

The equation of a circle is given by the formula

`\begin{gathered} (x-k)^2+(y-h)^2=r^2 \\ \text{center(origin)}=(0,0),r=6 \\ Equation=(x-0)^2+(y-0)^2=6^2_{} \\ =x^2+y^2=36 \end{gathered}`

ence, the equation of circle A centered at the origin with radius 6 is

x²+y²=36

2)Circle D with center (3, 3) and radius 2

The equation would be

`\begin{gathered} (x-3)^2+(y-3)^2=2^2 \\ =(x-3)^2+(y-3)^2=4 \end{gathered}`

ence, the equation of a circle D with center (,3, 3) and radius 2 is

(x-3)² + (y-3)² = 4