Circle equation question(s)

Question

So in this question, it is asking to graph a venn diagram with three circles. The equations I used are the followingL

E1: (x-h^2)^2+(y-k)^2=r^2

E2: (x-h)^2+(y-k)^2=r^2

E3: (x-h^1.5)^2+(y-k^2)^2=r^2.

The thing I am stuck on is when it asks me to choose two of the equations and solve as a system of equations, and how many solutions will be found when solved.

The second thing I cannot figure out is when it asks: how many solutions would you find if you were to solve all three equations as one system? How would you do this?

Thanks for any help!

Answer 1

Maybe this will help?

1. (x-1)² + (y +1)² = 9
2. x² + y² = 16
3. (x - 3)² + (y-1)² = 9
4. Using just two of these equations to solve the system of equations should give you 2 points of intersection for the two circles selected.
5. The steps are just to solve for one of the variables and plug into the 2nd one. So, solve for x as an example x = √(16-y²), then plug that equations into the first equation for x and solve for y. You should get y = 0, 4. Plug those two values into the x equation just solved and you should get x = 4, 0. So your intersections FOR JUST THOSE 2 CIRCLES are: (4,0) and (0,4).
6. Using all three equations to solve the system of equations (I think that's what was meant in the second question you posed above). You should get all three intersecting points for the three concentric circles.

I hope this helps and I was on the right "assumption" path for you.