**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. .

•** Solution**

(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)

S

X: [2xl sym]

y: [2xl sym]

»S.x

ans

9/2-1/8*bA2+1/8*(-16+24*bA2-bA4)A(1/2)] 9/2-1/8*bA2-1/8*(-16+24*bA2-bA4)A(1/2)]

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.

»subs(S.x,b,sqrt(3))

ans

4.9820

3.2680

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.

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