Question

trace the curve x^3+y^3=a^2x

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

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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