- #1
Niaboc67
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Homework Statement
The equation that is first listed is: 2x^2 + 2y^2 = 7
Homework Equations
The Attempt at a Solution
It's redefing the bottom portion therefore I think it's y=0,-2 because that is the range?
Equation for y to obtain an equation that represents circle
- Thread starter Niaboc67
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In summary, the conversation discusses a circle equation, 2x^2 + 2y^2 = 7, and finding the solution in the form of y = f(x) to match a given graph. The solution involves solving for y and considering the +/- symbol in front of the x term based on the plot.
The equation that is first listed is: 2x^2 + 2y^2 = 7
It's redefing the bottom portion therefore I think it's y=0,-2 because that is the range?
- #2
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I do not get how you think that is a solution. The solution is an equation in the form of y = f(x) such that it is represented by the graph shown (the lower portion of the circle. This is trivial.Niaboc67 said:
- #3
BvU
Science Advisor
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Is there something known about x that you forgot to tell us ?
- #4
RUber
Homework Helper
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If you use some algebra to solve the circle equation for y, you should have a ##\pm## symbol in front of the x part. You want to either choose + or - based on what the plot shows.
1. What is the general equation for a circle?
The general equation for a circle is (x - h)2 + (y - k)2 = r2, where h and k represent the coordinates of the center of the circle and r represents the radius.
2. How do you convert the equation for y to represent a circle?
To obtain an equation that represents a circle, you must first isolate the y variable on one side of the equation. This can be done by using algebraic operations such as addition, subtraction, multiplication, or division on both sides of the equation. Once y is isolated, the equation should have the form y = some expression involving x. This expression can then be substituted into the general equation for a circle to obtain the equation in terms of x.
3. Can you explain the meaning of the variables in the equation for a circle?
The variables h and k represent the coordinates of the center of the circle, which is the point where all radii of the circle intersect. The variable r represents the length of the radius, which is the distance from the center of the circle to any point on the circle's circumference.
4. How do you graph a circle using the equation for y?
To graph a circle using the equation for y, you can first plot the center point at (h, k) on the coordinate plane. Then, use the radius r to plot points on the circle's circumference by adding or subtracting r to/from the x-coordinate of the center point and solving for y. This will give you two points on the circle's circumference. Repeat this process for several values of x to plot more points and then connect them to form the circle.
5. What are some real-world applications of the equation for a circle?
The equation for a circle has many practical applications in fields such as engineering, physics, and geometry. It can be used to model the orbits of planets and satellites, calculate the area of circular objects, and design circular structures such as bridges and tunnels. It is also used in computer graphics to create smooth curves and circles on screens.
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