find the center and radius of the circle with the equation (x+1)^2 + (y-2)^2 = 16 . Then graph
the circle. (note the scale on the graph paper is going by 2s)
The center of the circle is at (-1, 2) because the equation is in the form (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center and r is the radius.
The radius of the circle is 4 because the equation is in the form (x - h)^2 + (y - k)^2 = r^2 and we can see that r^2 = 16.
To graph the circle, we can plot the center (-1, 2) as a point on the graph paper. Then we can count out 4 units in each direction from the center and plot those points to form the circle.
Here is the graph of the circle:
To find the center and radius of the circle with the equation (x+1)^2 + (y-2)^2 = 16, we can compare the equation to the general equation of a circle: (x-a)^2 + (y-b)^2 = r^2.
Comparing the given equation to the general equation, we can see that a = -1, b = 2, and r^2 = 16. Therefore, the center of the circle is (-1, 2) and the radius is 4.
To graph the circle on graph paper with a scale going by 2s, we'll first mark the center (-1, 2). Now, we need to plot points on the circumference of the circle.
We start by considering the x-coordinate of the center. From the center, we move 4 units to the right (since the radius is 4) and plot a point. From the center, we move 4 units to the left and plot another point. These points will be (-1+4, 2) = (3, 2) and (-1-4, 2) = (-5, 2) respectively.
Next, we consider the y-coordinate of the center. From the center, we move 4 units upwards and plot a point. From the center, we move 4 units downwards and plot another point. These points will be (-1, 2+4) = (-1, 6) and (-1, 2-4) = (-1, -2) respectively.
Finally, we connect these plotted points to form a circle shape.