I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the circle is : $\frac{1}{\sqrt{2}}$. I am given the points: $A(0,0)$, and $B(1,0)$. Let's consider the parameter $S$ such that when $S=0$, we are at the point $A$, and when $S=1$, we are at the point $B$. I need to parametrize the quarter of the circle that starts from A and ends at B, in terms of the parameter $S$ (i.e, I am trying to find $x(S)$ and $y(S)$). I tried many times, but I couldn't come up with expresions for $x(S)$ and $y(S)$ that satisfy the equation of the circle, and such that when $S=0$, we have : ($x=0$ and $y=0$), and when $S=1$, we have $x=1$ and $y=0$. Any help is appreciated!!!
parametrizing quarter of a circle
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calculus
real-analysis
analysis
multivariable-calculus
parametric