finding centre and radius

Question

find the centre and radius of the circle with segment of the line x + y = 1 cut off by coordinate axes as diameter

Answer 1

The x- and y- intercepts of the line x+y=1 are A=(1,0) and B=(0,1). These points are the endpoints of a diameter of the circle.

 

Center of circle = midpoint of AB = ((1+0)/2, (0+1)/2) = (1/2,1/2)

 

Radius of circle = distance from A to B = √[(0-1)²+(1-0)²] = √2

 

Equation of circle:  (x - 1/2)² + (x - 1/2)² = (√2)²

 

                           (x - 1/2)² + (x - 1/2)² = 2