Intersection of Two Circles
We want to find the intersection points of two circles. The first circle has a radius of 2 and is centered at x= 3, y = 5. The second circle has a radius b and is centered at x = 5,
y = 3. See Figure 10.2-1.
(a) Find the (x, y) coordinates of the intersection points in terms of the patameter b.
(b) Evaluate the solution for the case where b = /3. .
(a) The intersection points are found from the solutions of the two equations for the circles. These equations are
The session to solve these equations follows. Note that the result x: [2xl sym 1 indicates that there are two solutions for x. Similarly, there are two solutions for y.
»syms x y b
»8 = solve((x-3)A2+(y-5)A2-4. (X-5)A2+(y-3)A2-bA2)
X: [2xl sym]
y: [2xl sym]
The solution for the x coordinates of the intersection points is The solution for the y coordinates can be found in a similar way by typing S. y. (b) Continue the session by substituting b = -./3 into the expression for x.
Thus the x coordinates of the two intersection points are x = 4.982 and x = 3. The y coordinates can be found in a similar way.