Austin wants to sketch the graph of a circle represented by the given equation.
(x - 4)2 + (y + 7)2 = 64
Using complete sentences, describe the steps used to sketch the circle on a coordinate grid
Plot the center at (4,-7)
Plot the horizontal and vertical diameter endpoints, 8 units from the center.
Sketch a circular curve using those points.
Much easier with a compass :-)
To sketch the graph of a circle represented by the given equation (x - 4)² + (y + 7)² = 64, follow these steps:
1. Start by identifying the center of the circle: The equation is in the form (x - h)² + (y - k)² = r², where (h, k) represents the center point. In this case, the coordinates of the center are (4, -7). So, mark this point on your coordinate grid.
2. Determine the radius: The equation tells us that the radius squared is 64. Taking the square root of both sides, we find that the radius is √64 = 8. Measure a distance of 8 units from the center in all directions (up, down, left, and right) and mark these points on the grid. These points will lie on the circumference of the circle.
3. Connect the marked points: With all the points marked, draw a smooth curve that connects them. This curve represents the boundary of the circle.
4. Add any additional details: If required, you can label the center point and the radius on the graph to make it more informative. Remember to include appropriate scale markings on the axes of the coordinate grid.
By following these steps, you should have successfully sketched the graph of the circle represented by the given equation.