## Exploring the Heart Curve: (x^2 + y^2 – 1)^3 = x^2 y^3 on Desmos

The equation **(x^2 + y^2 – 1)^3 = x^2 y^3** might look intimidating at first glance, but it hides a beautiful and fascinating shape known as the **heart curve**. Using Desmos, a free online graphing calculator, we can visualize this curve and explore its characteristics.

### Graphing the Heart Curve on Desmos

**Open Desmos:**Go to and open the graphing calculator.**Enter the Equation:**In the input field, type the equation:**(x^2 + y^2 - 1)^3 = x^2*y^3**.**Adjust the View:**Zoom in and out using the mouse wheel or the zoom buttons. Pan the graph by dragging or using the arrow keys. You can also adjust the x and y-axis limits to focus on specific parts of the curve.

### Exploring the Heart Curve

As you graph the equation, you'll notice a **heart-shaped curve**. This shape is due to the complex interplay between the terms in the equation. Here are some interesting observations:

**Symmetry:**The curve is**symmetric**about the y-axis.**Singular Point:**The curve has a**singular point**at the origin (0,0). This means that the curve intersects itself at this point.**Asymptotes:**The curve has**asymptotes**which means it approaches certain lines but never actually touches them. These asymptotes are located at**y = ±1**.

### Further Exploration with Desmos

Desmos offers a wide range of tools for exploring the heart curve:

**Sliders:**You can introduce**sliders**for variables within the equation, allowing you to manipulate the curve in real-time. Try adding a slider for the power of 'y' and see how the curve transforms.**Coloring:**Use different colors to highlight specific parts of the curve or different features like its asymptotes.**Annotations:**Add text labels to explain different aspects of the curve or mark important points.

### Conclusion

The heart curve is a fascinating example of how seemingly complex mathematical equations can lead to beautiful and unexpected shapes. Desmos provides a powerful and intuitive platform to visualize, explore, and gain a deeper understanding of such mathematical concepts.