- #1
ironluis
- 2
- 0
I need your help for solved this. 
X^2+y^2=9
(x+3)^2+(y-3)^2=9
Please help me.
X^2+y^2=9
(x+3)^2+(y-3)^2=9
Please help me.
Solve System of Equations: X^2+y^2 and (x+3)^2+(y-3)^2=9
- Context: MHB
- Thread starter ironluis
- Start date
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Discussion Overview
The discussion revolves around solving a system of equations represented by two circles: X^2 + y^2 = 9 and (x + 3)^2 + (y - 3)^2 = 9. Participants explore both algebraic and geometric methods for finding the intersection points of these circles.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant seeks assistance in solving the system of equations.
- Another participant questions whether the problem should be approached algebraically or geometrically, noting the context of the forum.
- A suggestion is made to set the two equations equal to each other, expand, and simplify to find solutions.
- A geometric approach is proposed, emphasizing the importance of the distance between the centers of the circles and the implications for the number of solutions based on this distance.
- Another participant references a specific algorithm for solving the intersection of two circles, indicating its effectiveness based on personal experience.
Areas of Agreement / Disagreement
Participants express differing views on whether to solve the problem algebraically or geometrically, and there is no consensus on the preferred method for finding the solutions.
Contextual Notes
The discussion includes various assumptions about the geometric properties of circles and the implications of their intersection, which remain unresolved. The effectiveness of different approaches is also mentioned but not agreed upon.
- #2
Jameson
- 4,533
- 13
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?
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?
- #3
ironluis
- 2
- 0
Im sorry
- #4
Prove It
Gold Member
MHB
- 1,434
- 20
Notice both equations are equal to 9, so they are equal to each other. Set them equal to each other, expand, simplify...
- #5
MarkFL
Gold Member
MHB
- 13,284
- 12
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.
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.
- #6
johng1
- 234
- 0
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.
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.
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