Question 122053
the general equation for a circle is (x-h)^2+(y-k)^2=r^2 __ (h,k) is the center, r is the radius


7.  the radius is the distance between the center and any point on the circle
__ using the distance formula, r^2=(-7-(-5))^2+(6-3)^2 __ r^2=13
__ so the equation is (x-3)^2+(y+5)^2=13


8.  the center is the midpoint of the diameter __ ((10+2)/2,(-4+2)/2) __ (6,-1)
__ using the distance formula, r^2=(10-6)^2+(-4-(-1))^2 __ r^2=25
__ so the equation is (x-6)^2+(y+1)^2=25


9.  the second and third points have the same y-coordinate, so a line connecting them is horizontal
__ the midpoint of the line has the same x-coordinate as the center of the circle __ (-5+7)/2=1, so the center is (1,y)


all radii of a circle are equal, so (distance formula again) __ (1-6)^2+(y-3)^2=(1-7)^2+(y-2)^2
__ 25+y^2-6y+9=36+y^2-4y+4 __ -2y=6 __ y=-3
__ using the distance formula, r^2=(1-(-5))^2+(-3-2)^2 __ r^2=61
__ so the equation is (x-1)^2+(y+3)^2=61