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

AI Thread 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.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
2
Views
1K
Replies
3
Views
2K
Replies
8
Views
1K
Replies
24
Views
3K
Replies
3
Views
1K
Replies
1
Views
1K
Replies
6
Views
1K
Back
Top