1. **Problem Statement:** Create and label a flower design with circles using their standard equations. You will describe centers and radii and write the equation in the form $$ (x-h)^2 + (y-k)^2 = r^2 $$. 2. **Identify Circles:** - Center flower circle: center $(0,0)$, radius $5$ - Petal 1 circle: center $(5,0)$, radius $3$ - Petal 2 circle: center $(-5,0)$, radius $3$ - Petal 3 circle: center $(0,5)$, radius $3$ - Petal 4 circle: center $(0,-5)$, radius $3$ 3. **Write equations in standard form:** - Center flower: $$ (x-0)^2 + (y-0)^2 = 5^2 \implies x^2 + y^2 = 25 $$ - Petal 1: $$ (x-5)^2 + (y-0)^2 = 3^2 \implies (x-5)^2 + y^2 = 9 $$ - Petal 2: $$ (x+5)^2 + (y-0)^2 = 9 $$ - Petal 3: $$ (x-0)^2 + (y-5)^2 = 9 $$ - Petal 4: $$ (x-0)^2 + (y+5)^2 = 9 $$ 4. **Explanation:** Center $(h,k)$ gives each circle's midpoint; radius $r$ defines size. All petals are arranged symmetrically around the center flower, positioned $5$ units out along axes, making a balanced flower pattern. 5. **Reflection:** I positioned the centers symmetrically to create a floral arrangement and varied radii to distinguish the large center from smaller surrounding petals, applying circle equations to label each part clearly.