Which is the standard equation of a circle with radius $$ r $$ and center located at $$ (h, k) $$ ? $$ (x+h)^{2}+(y+k)^{2}=r^{2} $$ $$ (x-h)^{2}+(y+k)^{2}=r^{2} $$ $$ (x-h)^{2}+(y-k)^{2}=r $$ $$ (x-h)^{2}+(y-k)^{2}=r^{2} $$

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

$$
(x - h)^{2} + (y - k)^{2} = r^{2}
$$

Let's evaluate the provided options:

1. **$$(x + h)^{2} + (y + k)^{2} = r^{2}$$**  
   This equation incorrectly adds $$h$$ and $$k$$ instead of subtracting them. This would represent a circle centered at $$(-h, -k)$$.

2. **$$(x - h)^{2} + (y + k)^{2} = r^{2}$$**  
   This equation correctly subtracts $$h$$ but incorrectly adds $$k$$. This would represent a circle centered at $$(h, -k)$$.

3. **$$(x - h)^{2} + (y - k)^{2} = r$$**  
   While this equation correctly subtracts both $$h$$ and $$k$$, it incorrectly sets the right side to $$r$$ instead of $$r^{2}$$. The right side should be the square of the radius.

4. **$$(x - h)^{2} + (y - k)^{2} = r^{2}$$**  
   This is the correct standard form. It subtracts both $$h$$ and $$k$$ and sets the equation equal to $$r^{2}$$, accurately representing a circle with center $$(h, k)$$ and radius $$r$$.

**Correct Answer:**  
$$
(x - h)^{2} + (y - k)^{2} = r^{2}
$$

Which corresponds to the **fourth option**.
The correct standard equation of a circle with center at $$(h, k)$$ and radius $$r$$ is: $$ (x - h)^{2} + (y - k)^{2} = r^{2} $$ So, the correct choice is the fourth option.

Which is the standard equation of a circle with radius \( r \) and center located at \( (h, k) \) ? \( (x+h)^{2}+(y+k)^{2}=r^{2} \) \( (x-h)^{2}+(y+k)^{2}=r^{2} \) \( (x-h)^{2}+(y-k)^{2}=r \) \( (x-h)^{2}+(y-k)^{2}=r^{2} \)

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