Math Problem Statement
Solution
To eliminate the parameter and express the relationship between and in Cartesian form, we’ll start with the given parametric equations:
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Solve for in terms of from the second equation:
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Substitute into the first equation to express in terms of :
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Expand and simplify:
So, the Cartesian equation of the curve is:
Range of :
Given that , substituting into gives:
Thus, the Cartesian equation is:
Would you like more details on this or have any further questions?
Related Questions
- How can we find the range of for this curve?
- What is the vertex of the resulting parabola in terms of and ?
- How would the equation change if the parametric equations included a different transformation?
- Can we find the derivative of the curve given in Cartesian form?
- How do we plot the Cartesian form of this parametric equation?
Tip
When eliminating parameters, isolate the parameter in one equation and substitute it into the other to find the direct relationship.
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Math Problem Analysis
Mathematical Concepts
Parametric Equations
Cartesian Coordinates
Algebraic Manipulation
Formulas
x = t^2 - 2
y = t + 3
Theorems
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Suitable Grade Level
Grades 9-12
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