Is this equation cartesian equation?

Question

Is this equation a cartesian equation? :
4x^4 + y^2 = 4x^2

Thank u for answering, and if I wrote the same equation like these:
4x^4 -4x^2= -y^2 or
y^2 - (2x)^2 = -4x^4

those two are still cartesian, right?

Answer 1

Yes. Cartesian is measured using x and y, where x and y are respective "vectors" perpendicular to each other (and likewise in three dimensions, z would be mutually "perpendicular", or normal to x and y).

And yes, those two latter equations are still Cartesian.

Examples of non-Cartesian equations would include variables like:
Polar: (r, θ), where r is the radius (r² = x² + y²), and θ is the angle along the reference plane (θ = arctan(y/x)).

Cylindrical: (r, θ, z), where r is the radius (r² = x² + y²), θ is the angle along the reference plane (θ = arctan(y/x)), and z is the height above the reference plane (z = z).

Spherical: (ρ, θ, φ), where ρ is the radius (ρ² = x² + y² + z²), θ is the angle along the reference plane (θ = arctan(y/x)), and φ is the angle measured from the normal to the reference plane (φ = arccos(z/ρ)).

Answer 2

Yes, these equations can be plotted on a Cartesian coordinate system as the equation is expressed in x's and y's and the grid is a rectilinear one -- ie the unit vectors are perpendicular and form a unit cube or square. The other systems are for 2 dimensions are polar and for 3-dimensions spherical, cylindrical or Cartesian.

Answer 3

Sure...Cartesian coordinate systems just describe systems in a two-dimensional plane (or a 3-D volume I guess, but strictly speaking, they are limited to 2-D). The above is a two-dimensional curve.