Question

can someone help me write the equation for a circle with a diameter that has endpoints at (–4, –1) and (–8, –9).

Answer 1

equation of a circle is equal to :
\[(x-a)^2 + (y-b)^2 = r^2\]
where r = radius and (a,b) are coordinates of the centre of the circle

Answer 2

here your diameter's end points are (-4,-1) and (-8,-9)
meaning :
where c is the centre of the circle, which is also the midpoint of these 2 points