Final answer:
To graph the equation (x²+y²)²=2xy, rewrite it as x⁴ + y⁴ - 2xy - 2x²y² = 0 and plot points by substituting different values for x and y.
Step-by-step explanation:
To graph the equation (x²+y²)²=2xy, we can rewrite it in a different form that is easier to plot. Let's expand the left side:
(x²+y²)² = (x²+y²)(x²+y²) = x⁴ + 2x²y² + y⁴. Now the equation becomes x⁴ + 2x²y² + y⁴ = 2xy. We can rearrange this equation to get: x⁴ + y⁴ - 2xy - 2x²y² = 0.
This equation represents a curve called a quartic curve or a polynomial curve of degree 4. To graph this curve, we can plot points by substituting different values for x and y into the equation and solving for the resulting expression. By plotting enough points, we can sketch a reasonably accurate graph of the curve.