The equation of the circle in which P = (-3, -2) and Q = (1 , 6) are the endpoints of the diameter is given by:
(x + 1)² + (y - 2)² = 20
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center is the midpoint of the diameter, hence:
The radius is half the diameter, hence:
[tex]D = \sqrt{(6 - (-2))^2 + (1 - (-3))^2} = \sqrt{80} = 4\sqrt{5}[/tex]
[tex]r = \frac{D}{2} = 2\sqrt{5}[/tex]
[tex]r^2 = 20[/tex]
Hence the equation of the circle is:
(x + 1)² + (y - 2)² = 20
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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