Expert: Sherry Wallin - 8/27/2009

Question
Find the standard form for the equation of a circle with a diameter with ends points (-10. -6) and (7, -4)

Answer
Jonathan~
    To write the standard form of the equation of a circle you will need the radius and the center. You have enough info to get the diameter which we know is twice the radius. To get the diameter use the distance formula: sqrt((-10-7)^2+(-6-(-4))^2)= sqrt((-17)^2 + (-2)^2)= sqrt(289 + 4)= sqrt(293) which is approx 17. So the radius is about 8.5 (half of 17). To find the center of the circle use the midpoint formula: ((-10+7)/2, (-6 -(-4))/2 -> (-3/2, -2/2)-> (-3/2, -1) is the center. Thus the equation of this circle is (h-(-3/2))^2 +(k-(-1))^2 = (8.5)^2 or (h+3/2)^2 + (k+1)^2 = 72.25

Math Prof