trace the curve x^3+y^3=a^2x
Answers
Answer:
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Step-by-step explanation:
Equation of the curve in terms of x as a function of y is,
x = y^3 / (x^2 - a^2)
Equation of the curve in terms of y as a function of x is,
y = [(a^2x - x^3)^1/3].
Given:
The curve: x^3+y^3=a^2x, where a is a constant.
To find:
The equation of the curve in terms of y as a function of x.
Solution:
To obtain the equation of the curve in terms of y as a function of x, we first rearrange the given equation as follows:
y^3 = a^2x - x^3
Now, we can solve for y in terms of x by taking the cube root of both sides:
y = [(a^2x - x^3)^1/3]
This is the equation of the curve in terms of y as a function of x.
Alternatively, we can solve for x in terms of y by rearranging the given equation as follows:
x^3 = a^2x - y^3
Now, we can solve for x in terms of y by factoring out x on the right-hand side:
x(x^2 - a^2) = y^3
x = y^3 / (x^2 - a^2)
This is the equation of the curve in terms of x as a function of y.
Therefore, the equation of the curve x^3+y^3=a^2x in terms of y as a function of x is
y = [(a^2x - x^3)^1/3].
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