1. **Problem statement:** Graph a circle with center at $(1,0)$ that passes through $(-3,0)$. Find the area and circumference of the circle, both in terms of $\pi$ and to the nearest tenth using $3.14$ for $\pi$. 2. **Find the radius:** The radius $r$ is the distance from the center $(1,0)$ to the point $(-3,0)$ on the circle. $$r = |1 - (-3)| = |1 + 3| = 4$$ 3. **Equation of the circle:** The general form of a circle with center $(h,k)$ and radius $r$ is $$ (x - h)^2 + (y - k)^2 = r^2 $$ Substitute $h=1$, $k=0$, and $r=4$: $$ (x - 1)^2 + (y - 0)^2 = 4^2 $$ $$ (x - 1)^2 + y^2 = 16 $$ 4. **Find the circumference:** The formula for circumference $C$ is $$ C = 2 \pi r $$ Substitute $r=4$: $$ C = 2 \pi \times 4 = 8 \pi $$ Using $\pi \approx 3.14$: $$ C \approx 8 \times 3.14 = 25.12 $$ Rounded to the nearest tenth: $$ C \approx 25.1 $$ 5. **Find the area:** The formula for area $A$ is $$ A = \pi r^2 $$ Substitute $r=4$: $$ A = \pi \times 4^2 = 16 \pi $$ Using $\pi \approx 3.14$: $$ A \approx 16 \times 3.14 = 50.24 $$ Rounded to the nearest tenth: $$ A \approx 50.2 $$ **Final answers:** - Equation of the circle: $$(x - 1)^2 + y^2 = 16$$ - Circumference: $8\pi$ or approximately $25.1$ - Area: $16\pi$ or approximately $50.2$