circles

Question

The equation of a circle with center (h, k) and radius r is

RankGuru · Accepted Answer

1. **Definition**: A circle is the locus of a point $(x, y)$ that maintains a constant distance $r$ from a fixed point $(h, k)$.
2. **Apply Distance Formula**: $\sqrt{(x-h)^2 + (y-k)^2} = r$.
3. **Square Both Sides**: $(x-h)^2 + (y-k)^2 = r^2$.
4. **Result**: This is the 'Standard Form' of a circle's equation. If the center is at the origin $(0, 0)$, it simplifies to $x^2 + y^2 = r^2$.

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