Question: Return the original user prompt in the "prompt" field. Wrap every mathematical expression, number used in a calculation, equation, fraction, variable, or formula in $...$ for inline math or $$...$$ for display math.

1. **Problem Statement:** We are given the implicit curve defined by the equation $$ (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 $$. 2. **Understanding the Equation:** This is a well-known implicit equation that describes a heart-shaped curve called the "heart curve" or "heart-shaped implicit curve." It is not a function $y=f(x)$ explicitly, but an implicit relation between $x$ and $y$. 3. **Key Features:** - The curve is symmetric about the $y$-axis because the equation involves $x^2$ and $y^2$ terms. - The curve passes through points where the expression equals zero. 4. **Plotting and Visualization:** To visualize this curve, one would typically use implicit plotting techniques. 5. **No further algebraic simplification is needed** since the equation is already in implicit form. **Final answer:** The implicit curve is given by $$ (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 $$ which describes a heart-shaped curve centered near the origin.