1. **State the problem:** Write the standard form equation of the circle given its center and radius. 2. **Recall the standard form of a circle's equation:** $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h,k)$ is the center and $r$ is the radius. 3. **Problem 1:** The circle is centered at the origin $(0,0)$ with radius $1$. 4. Substitute $h=0$, $k=0$, and $r=1$ into the formula: $$ (x - 0)^2 + (y - 0)^2 = 1^2 $$ which simplifies to $$ x^2 + y^2 = 1 $$ 5. **Problem 3:** The circle is centered at approximately $(4,3)$ with radius $3$. 6. Substitute $h=4$, $k=3$, and $r=3$ into the formula: $$ (x - 4)^2 + (y - 3)^2 = 3^2 $$ which simplifies to $$ (x - 4)^2 + (y - 3)^2 = 9 $$ **Final answers:** - Problem 1: $$ x^2 + y^2 = 1 $$ - Problem 3: $$ (x - 4)^2 + (y - 3)^2 = 9 $$