graph the circle $x^2 + y^2 = 1$.\n\nplot the center. then plot a point on the circle. if you make a…

Explanation:

Step1: Identify the standard form of a circle

The standard equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. $$x^2 + y^2 = 1$$

Step2: Determine the center of the circle

Since there are no $h$ or $k$ values subtracted from $x$ and $y$, the center $(h, k)$ is at the origin. $$(h, k) = (0, 0)$$

Step3: Calculate the radius of the circle

The constant on the right side represents $r^2$. Take the square root to find $r$. $$r^2 = 1 \implies r = \sqrt{1} = 1$$

Step4: Identify points to plot on the circle

Move $r$ units from the center in any cardinal direction to find a point on the circumference. $$(0 + 1, 0) = (1, 0)$$

Answer:

To graph the circle, plot the center at $(0, 0)$ and a point on the circle at $(1, 0)$.