Answer:
(x+1)^2+(y+4)^2=16
Step-by-step explanation:
equation of the circle
(x-x0)^2+(y-y0)^2=r^2
where x0 and y0 is center of circle
and r is radius of the circle.
we know that the center point is the middle of the diameter
so x0=(x1+x2)/2
x0=(3+(-5))/2=-2/2=-1
y0=(-4+(-4))/2=-8/2=-4
so the midpoint or the center of circle is the points (-1,-4)
the formula to find the distance between two. points is √[(x2-x1)^2+(y2-y1)^2]
so r is the distance between the center point and one of the diameter endpoints.
let us take points (3,-4) and center point (-1,-4)
√(-1-3)^2+(-4-(-4))^2=
√(-4)^2+0^2=
√16=4
so the radius of the circle is 4
now the equation of the circle will be
(x-(-1))^2+(y-(-4))^2=4^2
(x+1)^2+(y+4)^2=16
