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In fact, equation (4) defines a double Archimedean spiral (changing $(x,y)$ into $(-x,-y)$ doesn't change this equation). See picture below where the red curve is the Archimedean spiral, strictly speaking, and the magenta curve is its copy through a central symmetry. Equation (4) is less manageable than (3).
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The equation of an object is a way of telling whether a point is part of an object -- if you substitute the coordinates of the point into the equation and the equation is true, then the point is on the object; if the equation is not true for that point, then the point is not on the object.
I'm trying to find the cartesian equation of the curve which is defined parametrically by: $$ x = 2\sin\theta, y = \cos^2\theta $$ Both approaches I take result in the same answer: $$ y = 1 - \s...
For example, the square can be described with the equation $|x| + |y| = 1$. So is there a general equation that can describe a regular polygon (in the 2D Cartesian plane?), given the number of sides
I am supposed to find a Cartesian equation by eliminating the parameters of ... This equation can be ...
Converting Polar Equation to Cartesian Equation. 0. Polar coordinate form of circle equation. 0.
Find the vector equation of the line with Cartesian equation: $$5x + 1 = -10y - 4 = 2z$$ I know the vector equation of a line is $\textbf{r} × \textbf{v} = \textbf{a} × \textbf{v}$, where $\textbf{r}$ is the position vector of a point on the line, $\textbf{a}$ is a fixed point on the line, and $\textbf{v}$ is a direction vector for $\textit{L ...
Parabola equation from cartesian to polar representation. 0. how to convert y=sin(6x)+2 to polar. 0.
EDIT1: What you at first proposed as ellipse looks like: The Ellipse parametrization is done differently. To more clearly distinguish between them we should note there are two different $\theta$ s, viz $\theta_{deLaHire}$ and the standard polar coordinate $\theta_{polar}$ used for central conics, ellipse in this case.