The endpoints of a diameter of the circle are (-1, -11) and (-17, -5). Determine the equation of the circle.

(x+9)² +(y+8)² = 73

Step-by-step 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

the correct is answer is a 9-sided polygon!

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