Question

circle a is centered at (1,2) and contains the point (5,5). select all the points that also lie on circle a. (-3,-1) (-2,-2) (0,5) (1,8) (4,6)

Explanation:

Step1: Calculate the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The center of the circle is $(x_1,y_1)=(1,2)$ and a point on the circle is $(x_2,y_2)=(5,5)$. So $r=\sqrt{(5 - 1)^2+(5 - 2)^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step2: Check each point

For point $(-3,-1)$: $d=\sqrt{(-3 - 1)^2+(-1 - 2)^2}=\sqrt{16 + 9}=5$.
For point $(-2,-2)$: $d=\sqrt{(-2 - 1)^2+(-2 - 2)^2}=\sqrt{9 + 16}=5$.
For point $(0,5)$: $d=\sqrt{(0 - 1)^2+(5 - 2)^2}=\sqrt{1+9}=\sqrt{10}
eq5$.
For point $(1,8)$: $d=\sqrt{(1 - 1)^2+(8 - 2)^2}=\sqrt{0 + 36}=6
eq5$.
For point $(4,6)$: $d=\sqrt{(4 - 1)^2+(6 - 2)^2}=\sqrt{9 + 16}=5$.

Answer:

$(-3,-1)$, $(-2,-2)$, $(4,6)$