Question

graph the circle with equation (x + 5)^2+(y - 1)^2 = 16. plot the center and then a point on the circle.

Explanation:

Step1: Identify the center of the circle

The standard - form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle. For the equation $(x + 5)^2+(y - 1)^2 = 16$, we have $h=-5$ and $k = 1$. So the center of the circle is $(-5,1)$.

Step2: Identify the radius of the circle

Since $(x + 5)^2+(y - 1)^2 = 16$ and $16=r^2$, then $r = 4$ (taking the positive square - root as radius is non - negative).

Step3: Find a point on the circle

We can find a point on the circle by moving a distance of the radius from the center. If we move 4 units to the right of the center $(-5,1)$, the $x$ - coordinate of the point will be $-5 + 4=-1$ and the $y$ - coordinate will remain the same, so a point on the circle is $(-1,1)$.

To graph:

1. Plot the center $(-5,1)$ on the coordinate grid.
2. Plot the point $(-1,1)$ on the coordinate grid.
3. Use a compass or free - hand to draw a circle with center $(-5,1)$ passing through the point $(-1,1)$.

Answer:

Center: $(-5,1)$; Point on the circle: $(-1,1)$