Question

enter the equation of a circle that is congruent to \\( \bigodot c \\) and is centered at point \\( p \\).

Explanation:

Step1: Identify center of $\odot C$

From the graph, center $C$ is at $(7, -3)$.

Step2: Find radius of $\odot C$

The circle reaches the x-axis at $x=10$, so radius $r = 10 - 7 = 3$.

Step3: Identify center of new circle

Point $P$ is at $(-6, 1)$.

Step4: Write circle equation

Use standard circle form $(x-h)^2+(y-k)^2=r^2$, where $(h,k)=(-6,1)$, $r=3$.
Expression: $(x - (-6))^2 + (y - 1)^2 = 3^2$
Simplify to: $(x+6)^2+(y-1)^2=9$

Answer:

$(x+6)^2+(y-1)^2=9$