Question: the circle c has equation $$(x-1)^2 + (y+4)^2 = 25$$ find centre and radius of c
1. **State the problem:** We are given the equation of a circle $$(x-1)^2 + (y+4)^2 = 25$$ and need to find its centre and radius.
2. **Recall the standard form of a circle's equation:**
$$ (x-h)^2 + (y-k)^2 = r^2 $$
where $$(h,k)$$ is the centre and $$r$$ is the radius.
3. **Identify the centre:**
From the given equation, compare with the standard form:
- $$h = 1$$ (note the sign changes inside the parentheses)
- $$k = -4$$
So, the centre is $$(1, -4)$$.
4. **Find the radius:**
The right side of the equation is $$25$$, which equals $$r^2$$.
So,
$$ r = \sqrt{25} = 5 $$.
**Final answer:**
- Centre: $$(1, -4)$$
- Radius: $$5$$