Find the circle centered at (t,−1) and passing through (t+3,3).
- In x²+y²+Dx+Ey+F=0, a nondegenerate circle requires (D²+E²)/4−F>0.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Translate the geometric condition into a coordinate equation.
Hint 2
Use this intermediate relation.
Worked solution
Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
Use the center-to-point distance; the point itself is not the center.
The requested relation or conclusion is shown below.
Checks and common pitfalls: Use the center-to-point distance; the point itself is not the center.
Reasoning checklist · self / teacher assessment
- State a valid definition or model and its assumptions.
- Show the intermediate mathematical relations, not only the final claim.
- Check exclusions, units or the interpretation of the result.
Think first. Reveal a hint when the class is ready.