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Step-by-step explanation:

The diameter of the circle is the distance from the endpoint to another endpoint. The diameter of the given circle is segment PQ. To determine the diameter of the circle, we would apply the formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Therefore,

Diameter = √(1 - - 3)² + (9 - 5)²

Diameter = √4² + 4² = √32

Radius = diameter/2 = √32/2

A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.

The center of the circle is determined by applying the midpoint formula

(x1 + x2)/2, (y1 + y2)/2

= (- 3 + 1)/2, (5 + 9)/2

Center = (- 1, 7)

The formula for determining the equation of a circle us expressed as

(x - h)² + (y - k)² = r²

Where

r represents the radius of the circle

h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,

h = - 1 and k = 7

Substituting into the formula, it becomes

(x - h)² + (y - k)² = r²

(x - - 1)² + (y - 7)² = (√32/2)²

(x + 1)² + (y - 7)² = 32/4

(x + 1)² + (y - 7)² = 8

goog may be able to you find that answer