Coordinate algebra question?

Question

Determine whether point A lies on the circle whose center is point C and which contains the Point P. 

Point a (3,2) 
Point c (-1,-1) 
Point p (4,-1) 

What is the radius? 

Does point A lie on the circle? 


Thanks a lot!!!

 

 

Answer 1

Circle contains the point P .

Circle center C (h, k ) = (- 1, -1) and P (4, -1).

The distance between center and the point is would be the radius of circle.

Radius (r ) = sqrt [(x -h )² + (y -k )²].

Substitute the values of  (h, k ) = (- 1, -1) and (x , y ) = (4, -1) in (r ) = sqrt [(x -h )² + (y -k )²].

r = sqrt [(4 + 1)² + (-1 + 1)²]

= sqrt [(5)² + (0)²]

= sqrt [25 + 0 ]

= sqrt [25].

= 5

Circle equation is (x - h )² + (y - k )² = r ².

(x + 1 )² + (y + 1 )² = (5) ²

(x + 1)² + (y + 1 )² =  25

x ² + 2x + 1 + y ² +2y + 1 = 25

x ² + y ² + 2x + 2y + 2 - 25 = 0.

Circle equation is x ² + y ² + 2x + 2y - 23 = 0.

Radius of the circle = 5.

The point A (3,2) = (x, y )

Circle equation x ² + y ² + 2x + 2y - 23 = 0.

3 ² +2 ² + 2(3) + 2(2) - 23 = 0

9 + 4 + 6 + 4 -23 = 0

23 - 23 = 0

0 = 0

So A  satisfy the circle equation.

The point A  lies on the circle.