Question

The points (-18,15) and (-20,15) lie on a circle with a radius of 1. Find the coordinates of the center of the circle.

Answer 1

.hello :
an equation of the circle Center at the w(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : r = 1
The points (-18,15) and (-20,15) lie on a circle with a radius of 1:
(-18-a)²+(15-b)² = 1 ....(1)
(-20-a)² +(15-b)² = 1 ....(2)
solve this system :
(1) -(2) : (-18-a)² - (-20-a)² =0
(-18-a)² =(-20-a)² =0
( -18-a = -20-a) or (-18-a = - (-20-a))
1 )  ( -18-a = -20-a) no solution confused : -18=-20
2 ) -18-a =20+a
      -2a =38
      a = -19 
subst in (1) :(-18+19)²+(15-b)² =1
(15-b)² = 0.... 15-b = 0     .... b = 15
the center is :w(-19,15)