Hi Sandra,

First you need to find the equations of each of the circles then you need to solve the system of equations. I'll use a similar example where the equations are already found:

(x - 2)² + (y - 5)² = 25

(x - 6)² + (y - 13)² = 65

First expand the binomials and collect like terms to one side of the equation:

x²-4x+4 + y² -10y+25=25 ⇒x²-4x+y² -10y+4=0 (Eq. 1)

x²-12x+36+y²-26y+169=65 ⇒ x²-12x+y²-26y+140=0 (Eq. 2)

Since both equations now equal 0, we can set them equal to each other:

x²-4x+y² -10y+4=x²-12x+y²-26y+140

Next collect like terms

8x+16y-136=0

then solve for a variable

8x=136-16y

x=17-2y (Eq. 3)

Substitute into one of the expanded equations (I choose eq. 1)

x²-4x+y² -10y+4=0 ⇒ (17-2y)²-4(17-2y)+y² -10y+4=0 ⇒ 289-68y+4y²-68+8y+y²-10y+4=0

and then collect like terms

5y²-70y+225=0

We can factor this binomial and then find the roots

5(y²-14y+45)=0

5(y-9)(y-5)=0 ⇒ y=9 and y=5

these are the y-values of our intersection points. to find the corresponding x-values, substitute into Eq.3

x=17-2(9)=-1

x=17-2(5)=7

So our intersection points are (-1,9) & (7,5)

Hope this helps,

Janice