# SOLUTION: Endpoints of a diameter: (-1, -6) (1, 6)

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 Geometry: Circles and their properties Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Circles Question 627051: Endpoints of a diameter: (-1, -6) (1, 6)Answer by jim_thompson5910(28696)   (Show Source): 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) --------------------------------------------------- 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 . -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------