SOLUTION: Find the equation of the circle with the diameter AB, given that the coordinates of A and B are (-6,1) and (4,-5). The equation of the circle should be written in the form (x-h)s

Question 581654: Find the equation of the circle with the diameter AB, given that the coordinates of A and B are (-6,1) and (4,-5).
The equation of the circle should be written in the form (x-h)squard + (y-k))squared =radius squared
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that the general equation of a circle is .

So we need the center (h,k) and the radius squared .

First, let's find the center (h,k).

Since the center is the midpoint of the line segment with endpoints (-6,1) and (4,-5), we need to find the midpoint.

X-Coordinate of Midpoint =

Since the x coordinate of midpoint is , this means that

Y-Coordinate of Midpoint =

Since the y coordinate of midpoint is , this means that

So the center is the point (-1, -2)

---------------------------------------------------

Now let's find the radius squared

Use the formula , where (h,k) is the center and (x,y) is an arbitrary point on the circle.

In this case, and . Also, and . Plug these values into the equation above and simplify to get:

So because , , and , this means that the equation of the circle that passes through the points (-6,1) and (4,-5) (which are the endpoints of the diameter) is

.

So the answer is

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