Answer:
( x + 5 )² + ( y - 3 )² = 52
Step-by-step explanation:
Let find the equation of the line going through A( - 11, 7 ) and B( - 9, - 3 )
m = [tex]\frac{-3-7}{-9+11}[/tex] = - 5
y - 7 = - 5( x + 11 )
y = - 5x - 48
Now, let find the equation of the line passing through midpoint of the segment AB
Coordinates of that midpoint is ( [tex]\frac{-11-9}{2}[/tex] , [tex]\frac{7-3}{2}[/tex] ) = ( - 10 , 2 )
Slope of the perpendicular line is [tex]\frac{1}{5}[/tex] ( opposite reciprocal of ( - 5 )
y - 2 = [tex]\frac{1}{5}[/tex] ( x + 10 )
y = [tex]\frac{1}{5}[/tex] x + 4 ........... (1)
Coordinates of an intersection of two lines (1) and x = - 5 are coordinates of the center of the circle
y = [tex]\frac{1}{5}[/tex] ( - 5 ) + 4 = 3 ⇒ y = 3
O( - 5 , 3 ) is the center
The last!! RADIUS which is OA or OB
r = [tex]\sqrt{(-5+11)^2 +(3-7)^2}[/tex] = √52
( x + 5 )² + ( y - 3 )² = 52
