If the endpoints of the diameter of a circle are (8, 6) and (2, 0), what is the standard form equation of the circle?

Step-by-step explanation:

Here, the endpoints of the diameter of a circle are (8, 6) and (2, 0),

The center of the circle = Mid point of the line segment that shows the diameter

= Mid point of  (8, 6) and (2, 0),

=

=

= ( 5, 3 )

Now, the diameter of the circle = Distance of the points (8,6) and (2,0)

=

=

= unit

⇒ The radius of the circle = 3√2 unit

Since, the standard form equation of the circle is (x-h)² + (y-k)² = r²

Where (h,k) is the center of the circle and r is the radius of the circle,

Hence, The standard form of the given circle is,

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