- #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
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- Thread starter ironluis
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In summary, the conversation is about solving a system of equations that represent two circles. One approach is to set the equations equal to each other and solve algebraically, while another is to use a geometric approach by considering the midpoint between the centers of the circles and finding the points of intersection. The final solution can be found by finding the points on the line perpendicular to the segment connecting the centers that satisfy either of the equations.
- #2
Jameson
Gold Member
MHB
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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
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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
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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
- 235
- 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.
FAQ: Solve System of Equations: X^2+y^2 and (x+3)^2+(y-3)^2=9
What is a system of equations?
A system of equations is a set of two or more equations that contain the same variables. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system.
How do I solve a system of equations?
There are various methods for solving a system of equations, including substitution, elimination, and graphing. In this particular example, substitution would be the most efficient method.
What does the equation x^2 + y^2 represent?
This equation represents a circle centered at (0,0) with a radius of 1. This is because when x = 0, y can be any value between -1 and 1 (since -1^2 and 1^2 both equal 1). Similarly, when y = 0, x can be any value between -1 and 1. This creates a circle when all possible combinations of x and y are graphed.
How do I use substitution to solve this system of equations?
To use substitution, solve one of the equations for one of the variables (in this case, either x or y) and substitute that expression into the other equation. This will create an equation with only one variable, which can then be solved for its value. That value can then be substituted back into the original equation to find the other variable's value.
What is the solution to this system of equations?
The solution to this system of equations is x = -1 and y = 0. This can be found by substituting x = -1 into the second equation, which simplifies to y = 3. Therefore, the solution is (-1, 0).