A circle in center-radius form gives its center and radius through . Graph the equation in Desmos, then compare each point’s distance from the center with the radius. Points directly right or up are quick to check. For a diagonal point, count both coordinate changes; a point on the edge is not outside.
Hints
- Hint 1
In center-radius form, , the center is . Read as so you don't miss the negative center coordinate. What number squared gives ?
- Hint 2
A radius runs from the center to the edge. A point exactly one radius directly right or directly up is on the circle, not outside it. Check the points that share a coordinate with the center.
- Hint 3
For a diagonal point, its squared distance from the center is the sum of the squared horizontal and vertical changes. Compare that sum with , not ; outside means the sum is greater.
Step-by-step
Read the circle, then test the points
Step 1Graph the circle
Type into Desmos as written. It draws the circular edge; you don't need to solve for .
- Step 2
Find the center and radius
In center-radius form, , the center is and the radius is the center-to-edge distance . Here means , so the center is . Since , the radius is .
- Step 3
Check the points one radius away
From the center, is units directly right, and is units directly up. Each is exactly one radius away, so both are on the circle, not outside it.
- Step 4
Check the nearby point
The point is only unit directly right of the center. That's less than the radius of , so this point is inside the circle.
- Step 5
Test the diagonal point
For , the horizontal change from the center is and the vertical change is . Type ; Desmos prints . This is the point's squared distance from the center. Both coordinate changes count for a diagonal point. Since , the point is outside the circle. Choice C.