(x^2+y^2)^2=4(x^2-y^2)
Equation of a lemniscate curve
I think your are right, it is.
(x^2+y^2)^2=4(x^2-y^2)
Equation of a lemniscate curve ?! Can you solve this
To understand the equation of a lemniscate curve, let's break down the given equation:
First, notice that we have an expression on the left side of the equation: (x^2 + y^2)^2. This expression represents the square of the distance from the point (x, y) to the origin (0, 0).
On the right side of the equation, we have 4(x^2 - y^2), which represents the square of the difference between the distances of the point (x, y) to the x-axis and y-axis, respectively.
Combining these two expressions, the equation (x^2 + y^2)^2 = 4(x^2 - y^2) represents the condition where the square of the distance from a point (x, y) to the origin is equal to four times the square of the difference between its distances to the x-axis and y-axis.
This equation describes a specific type of curve known as a lemniscate. A lemniscate is a figure-eight-shaped curve, symmetrical about both the x and y-axes, with the origin in the center. It is characterized by the property that the distances from any point on the curve to the x-axis or y-axis differ by a fixed value.
In other words, the equation (x^2 + y^2)^2 = 4(x^2 - y^2) represents a lemniscate curve.