If the equation of a circle is (x + 4)2 + (y - 6)2 = 25, its radius is
5
10
25 user: find the distance between the points: (–6, 7) and (–1, –5). in your final answer, include the formula and calculations that you used to find the distance.

Equation fo a circle:
Data:
Center: C(x₀,y₀).
radius: r

(x-x₀)²+(y-y₀)²=r²

In this equation:
(x+4)²+(y-6)²=25
C(-4,6)
r²=25  ⇒r=√25=5

Then, it´s radius is 5.

If, we have got two points:
A(x₁,y₁)
B(x₂,y₂)
The distance beetween the points is:
dist(A,B)=√[(x₂-x₁)²+(y₂-y₁)²]

Then:
A(-6,7)
B(-1,-5)

dist(A,B)=√[(-1+6)²+(-5-7)²]
dist (A,B)=√(5²+12²)
dist (A,B)=√(25+144)
dist (A,B)=√169
dist (A,B)=13

the distance between the points (-6,7) and (-1,-5) is 13.