Find the center of the circle that passes through the points (1,3), (3,-2), (5,3).

Guest Nov 11, 2019

#1**+2 **

Using the formula for a circle (x-h)^2 + (y-k)^2 = r ^2

for the first point this becomes (1-h)^2 + (3-k)^2 = r^2

for the second point , this becomes (3-h)^2 +(-2-k)^2 = r^2 these are both equal to r^2, so equate them

then expand, collect 'like' terms and simplify to

4h-10k-3=0 (1)

Do all of this to the THIRD set of points and equate to the second set of points (red above)

expand and simlify to

4h+10k-21 =0 (2)

solve (1) and (2) for h,k = ** 3, 9/10**

then use distance formula from the center (3,9/10) to any of the three points to find r^2 = 8.41

(x-3)^2 + (y-9/10)^2 = 8.41

ElectricPavlov Nov 11, 2019