A diameter goes through a circle’s center, so its endpoints give you the center and radius. Name the endpoints in Desmos, use midpoint to find the center, and use distance to find the radius. Then write the circle in standard form. The key trap is putting the whole diameter on the right side, where the radius squared belongs.
Hints
- Hint 1
A midpoint sits halfway between two endpoints. Because the given segment is a diameter, its midpoint is the circle’s center. Which Desmos command finds that point from two named endpoints?
- Hint 2
The distance between the endpoints spans the whole circle. A radius goes only from the center to the edge, so it is half that distance. What should you divide by ?
- Hint 3
In standard form, , is the center. The right side is the radius squared, and the signs inside the parentheses are opposite the center’s coordinates.
Step-by-step
Find the midpoint and half-distance
Step 1Find the center
The given endpoints are the ends of a diameter, a segment through the center. The midpoint of a diameter is the circle’s center. Name the endpoints and in Desmos, then type . Click the plotted midpoint: Desmos shows , the center.
- Step 2
Find the radius
Type . Desmos prints . The distance between and is the entire diameter, so half of it is the radius: . Don’t put the diameter on the right side of the equation; that side needs .
- Step 3
Write the circle’s equation
In standard form, , the center is and the radius is . Put them into the equation, keeping the minus signs in the form:
Simplify :
Square the radius:
That is the circle’s equation. Choice B.