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 $(-5, -5)$.

Step2: Find radius of $\odot C$

The circle reaches from $x=-5$ to $x=0$ on the x-axis, so radius $r = |0 - (-5)| = 5$.

Step3: Identify center of new circle

Point $P$ is at $(5, -5)$.

Step4: Write circle equation

Use standard circle formula $(x-h)^2+(y-k)^2=r^2$, where $(h,k)=(5,-5)$, $r=5$.
$$(x-5)^2+(y+5)^2=5^2$$
Simplify the right-hand side:
$$(x-5)^2+(y+5)^2=25$$

Answer:

$\boldsymbol{(x-5)^2+(y+5)^2=25}$