Answer:
Place a point at ordered pair (3, -1); count 5 units in various directions because the equation has a 5-unit radius and plot these points; and connect the plotted points not including the center by drawing a circle that crosses through them. Reference image below!
Step-by-step explanation:
The equation (x - 3)² + (y + 1)² = 25 is in the equation form matching that of a circle which is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and the r represents the radius of the circle (in units).
With this, we can derive where the center is, and how many units each plotted point should be away from the center.
From the equation we can see variable h is 3. The addition operation (+) in the second binomial indicates that the negative that was previous in its place was distributed to a negative number, so our variable k must be a -1, this can be proven with:
(y - (-1))²
-(-1) = -1(-1) = 1
(y + 1)²
This means the center for this equation is at point (3, -1)
Now because r² = 25 in the original equation, we square root both in order to find the radius:
r² = 25
√(r²) = √25
r = 5
The radius is 5 units long.
This this information, we plot a point at (3, -1) to indicate our center and count 5 units in different directions, then, create a circle that intercept through each point:
To find a point 5 units away to the right of center (3, -1), add 5 units to the x-value while maintaining the y-value. 3 + 5 = 8, so we drop a point at (8, -1)
To find a point 5 units away to the left of center, subtract 5 units from the x-value while maintaining the y-value. 3 - 5 = -2, so we drop a point at (-2, -1).
To find a point 5 units above the center, we add 5 units to its y-value while maintaining the x-value. -1 + 4 = 4, so we drop a point at (3, 4).
To find a point 5 units below the center, we subtract 5 units from the y-value while maintaining the x-value. -1 - 5 = -6, so we drop a point at (3, -6).
Now, to connect these points, draw a circle that intercepts them. Make sure to exclude the center point. An example is attached in the image below!