Answer:
(x+9)² +(y+8)² = 73
Explanation:
The standard form of equation of a circle is expressed as;
(x-a)² +(y-b)² = r²
(a,b) is the centre of the circle
r is the radius
Get the midpoint;
Given the coordinate (-1, -11) and (-17, -5).
a= x1+x2/2
b = y1+y2/2
a = -1-17/2
a = -18/2
a = -9
b = -11 - 5/2
b = -16/2
b = -8
Get the diameter using the distance formula
d = √(y2-y1)² +(x2-x1)²
d = √(-5+11)² +(-17+1)²
d = √(6)² +(-16)²
d = √36+256
d = √292
r = d/2
r = √292/2
r² = 292/4
r² = 73
Get the equation
Recall rhat
(x-a)² +(y-b)² = r²
(x+9)² +(y+8)² = 73