Answer:
x² + y² = 17
Explanation:
The standard equation of a circle is :
(x -h)² + ( y -k) ²= r², where (h, k) are the a coordinate of the center of the circle and r is the radius of the circle
If the end point of diameter has the coordinates (-4,-1) and (4,1) then the center is at the origin so we have (h= 0, k= 0)
The radius is half of the diameter so is the distance form (0,0) to (4, 1).
We can use Pythagorean Theorem to find r²
r ² = 4²+1² = 17
(x -h)² + ( y -k) ²= r², substitute what we found out
(x -0)² + ( y -0) ²= 17
x² + y² = 17
This is the equation of the circle given characteristics end point of diameter (-4,-1) , (4,1)