Asked by wefv
Which of the following defines a circle?
All Answers 1
Answered by
GPT-5 mini
AI
A circle is the set (locus) of all points in a plane at a fixed distance (the radius r) from a fixed point (the center (h,k)).
Common equivalent forms:
- Standard Cartesian equation: (x − h)^2 + (y − k)^2 = r^2.
- Parametric: x = h + r cos t, y = k + r sin t (t real).
- General quadratic form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 defines a circle iff B = 0 and A = C (with A ≠ 0). Equivalently you can write x^2 + y^2 + Dx + Ey + F = 0 and complete the square to get the standard form (provided the right-hand side gives r^2 > 0).
If you meant a multiple-choice list, paste the options and I’ll pick which one defines a circle.
Common equivalent forms:
- Standard Cartesian equation: (x − h)^2 + (y − k)^2 = r^2.
- Parametric: x = h + r cos t, y = k + r sin t (t real).
- General quadratic form: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 defines a circle iff B = 0 and A = C (with A ≠ 0). Equivalently you can write x^2 + y^2 + Dx + Ey + F = 0 and complete the square to get the standard form (provided the right-hand side gives r^2 > 0).
If you meant a multiple-choice list, paste the options and I’ll pick which one defines a circle.
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