MHB Solve System of Equations: X^2+y^2 and (x+3)^2+(y-3)^2=9

Click For Summary
The discussion focuses on solving a system of equations represented by two circles, X^2 + y^2 = 9 and (x + 3)^2 + (y - 3)^2 = 9. Participants suggest both algebraic and geometric methods for finding the intersection points of the circles. A geometric approach involves analyzing the distance between the circle centers and their radii to determine the number of solutions. The midpoint between the circle centers is also highlighted as a key point for finding solutions along a perpendicular line. Ultimately, both algebraic and geometric strategies can effectively yield the intersection points of the given equations.
ironluis
Messages
2
Reaction score
0
I need your help for solved this. :confused:

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

Please help me.
 
Mathematics news on Phys.org
Re: I need help!

Hi ironluis,

Welcome to MHB! (Wave)

Is this a question about systems of equations? Are you supposed to look at the two equations and solve for $x$ and $y$? This can be done algebraically however you posted the question in our geometry forum. Are you supposed to solve it geometrically?
 
Im sorry :confused:
 
Notice both equations are equal to 9, so they are equal to each other. Set them equal to each other, expand, simplify...
 
A more geometric approach would be to consider the point midway between the center of the circles. We use the mid-point in this case because the radii of the circles is the same. If the distance of this midpoint to the radii is greater than the radii, then there is no solution. If this distance is equal to the radii, there is one solution, and if it is less than the radii, and greater than zero, then there are two solutions. If the distance is zero, then the circles are concurrent and there are an infinite number of solutions.

Next, compute the slope of the line segment connecting the center of the circles, and observe that the solutions will lie along the line perpendicular to this segment, and passing through the mid-point of the centers.

This line will give you the result suggested by Prove It's much more straightforward algebraic approach.

Then you want to find the points on this line which satisfy either of the equations describing the circles.
 
Hi,
I think the best geometric solution to the problem of intersection of two circles is given at Circle, Cylinder, Sphere
I have used this algorithm with good success.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
  • · Replies 1 ·
Replies
1
Views
1K
MHB -2.4.27 find center and radius of circle
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Adding 'z' to 2D graph equation
  • · Replies 3 ·
Replies
3
Views
2K
MHB 2.4.10 3 circles one intersection
  • · Replies 8 ·
Replies
8
Views
2K
High School Natural Numbers contain all the Primes
  • · Replies 24 ·
Replies
24
Views
3K
MHB Solve System of 2 Variables: $x^5+y^5=33,\,x+y=3$
  • · Replies 3 ·
Replies
3
Views
1K
MHB Solving System of Equalities: x^2-y\sqrt xy & y^2-x\sqrt xy =3
  • · Replies 2 ·
Replies
2
Views
1K
MHB Mason's question via Facebook about solving a system of equations (2)
  • · Replies 1 ·
Replies
1
Views
10K
MHB System of Equations: Find Triples $(x,y,z)$
  • · Replies 1 ·
Replies
1
Views
1K
MHB -6.1.12 solve for x 3^{2x}=105
  • · Replies 6 ·
Replies
6
Views
1K