You can
put this solution on YOUR website!I'm assuming you want to find the equation of the circle.
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 (-1,-6) and (1,6), 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 (0, 0)
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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 (-1,-6) and (1,6) (which are the endpoints of the diameter) is
.
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