Intersection point of two circles

Question

Solve the following systems of two circles by finding the intersection point(s), if any, algebraically.

 

x^2 + y^2 = 9

(x-3)^2 + (y+3)^2 = 9

Answer 1

x² + y² = 9

x² - 6x + 9 + y² + 6y + 9 = 9

 

Subtract the equations to get:  6x - 6y - 18 = 0

 

So, x - y = 3

 

Therefore, y = x - 3

 

Replace y by x - 3 in the equation x² + y² = 9

 

x² + (x-3)² = 9

 

x² + x² - 6x + 9 = 9

 

2x² - 6x = 0

 

2x(x - 3) = 0

 

x = 0 or x = 3

 

If x = 0, then y = x - 3 = -3

If x = 3, then y = x - 3 = 0

 

Intersection points:  (0, -3) and (3, 0)