4.
a. show that
(x − 2)(x − 6) + (y − 5)(y + 11) = 0
is the equation of a circle. what is the center of this circle? what is the radius of this circle?
b. a circle has diameter with endpoints (aa, and (cc, dd). show that the equation of this circle can be
written as
(x − a)(x − c) + (y − − d) = 0.

a) b) (a,b) (c, d) As long as (a,b) and (c,d) are the endpoints of of the diameter.

Step-by-step explanation:

a)

1) The reduced formula of the Circumference is given by:

2) Let's expand the factored one into one closer to the pattern above:

3) Completing the square for both trinomials:

4) In the Reduced Formula, ,

b) Using the previous example to show this:

When we  factor this way

We are indeed, naming "a" and "b", the coordinates of (a, b) of the first endpoint and "b" and "d" the second endpoint as well.Id est, D (2, 5) and B (6,-11).

The radius, is

So yes, the equation of the circle can be written as

As long as (a,b) and (c,d) are the endpoints of of the diameter.

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step-by-step explanation: