Question

Two points on a circle are points A(-11,7) and B(-9,-3)

1. Determine the equation of a lone containing the center of the circle

2. If the x-coordinate of the center is -5, determine the circle's center: (-5,?)

Answer 1

( x + 5 )² + ( y - 3 )² = 52

Explanation:

Let find the equation of the line going through A( - 11, 7 ) and B( - 9, - 3 )

m =
`(-3-7)/(-9+11)` = - 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 (
`(-11-9)/(2)` ,
`(7-3)/(2)` ) = ( - 10 , 2 )

Slope of the perpendicular line is
`(1)/(5)` ( opposite reciprocal of ( - 5 )

y - 2 =
`(1)/(5)` ( x + 10 )

y =
`(1)/(5)` x + 4 ........... (1)

Coordinates of an intersection of two lines (1) and x = - 5 are coordinates of the center of the circle

y =
`(1)/(5)` ( - 5 ) + 4 = 3 ⇒ y = 3

O( - 5 , 3 ) is the center

The last!! RADIUS which is OA or OB

r =
`√((-5+11)^2 +(3-7)^2)` = √52

( x + 5 )² + ( y - 3 )² = 52