Ryan’s teacher asked him to graph circle E with equation (x – 5)2 + y2 = 25. Below is the graph he submitted.
Circle E that contains points 30, 0; 5, negative 25; negative 20, 0; 5, 25.
What, if anything, did Ryan do wrong when graphing this equation?
His circle satisfies
(x-5)^2 + y^2 = 25^2
not just 25.
From the given equation of the circle, (x – 5)² + y² = 25, we can determine the center and the radius of the circle. The general equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the general equation, we can see that the center of Circle E is (5, 0) and the radius is 5.
Now let's analyze the points provided to check if Ryan graphed the circle correctly:
1. Point (30, 0): This point lies outside the circle. The x-coordinate is too far to the right, indicating that the graph is incorrect.
2. Point (5, -25): This point lies on the circle. The x-coordinate is correct, but the y-coordinate is negative. The graph should represent the point as (5, 25) since the equation involves y².
3. Point (-20, 0): This point lies outside the circle. The x-coordinate is too far to the left.
4. Point (5, 25): This point lies on the circle. The coordinates are correct.
Based on the analysis, Ryan made two mistakes when graphing Circle E: incorrectly representing the y-coordinate for point (5, -25) and incorrectly plotting point (30, 0) outside the circle.
To fix his mistakes, Ryan should correct the y-coordinate for point (5, -25) to (5, 25) and remove point (30, 0) from the graph since it lies outside the circle.