Final Answer:
The equation of the tangent line to the curve when y = -1 is x^2 - 1 = 0.
Explanation:
In order to find the equation of the tangent line to the curve when y = -1, we first need to find the derivative of the given equation. Taking the derivative with respect to x, we get 2xy - 3y^2. Substituting y = -1, we get 2x(-1) + 3(-1)^2 = 2x + 3. Rearranging the equation, we get x^2 - 1 = 0. This is the equation of the tangent line to the curve when y = -1.
To find the equation of the tangent line, we first need to find the derivative of the given equation. The derivative of the equation is found by using the power rule of derivatives which states that the derivative of a polynomial is the coefficient of the term multiplied by the power of the term minus one. Applying this rule to the given equation, we get 2xy - 3y^2.
Substituting the value of y with -1, we get 2x(-1) + 3(-1)^2 = 2x + 3. Rearranging the equation, we get x^2 - 1 = 0. This is the equation of the tangent line to the curve when y = -1.
To find the equation of the tangent line for any other value of y, we can follow the same procedure. First, we need to take the derivative of the given equation. Then, we need to substitute the desired value of y to get the equation of the tangent line.