B.2.2.16 ok wanted of modify this graph to be this......

[karush]

\begin{tikzpicture}
[declare function = {radius(\phi)=sqrt((3*sin(\phi)+cos(\phi)) / (sin(\phi)^3 -cos(\phi)^3)); },]

\draw[->] (-3,0) -- (3.4,0);
\draw[->] (0,-2) -- (0,4.2);

\draw[domain=50:{atan(-1/3)+179.99}, variable=\phi, red, smooth, ultra thick] plot ({radius(\phi) * cos(\phi)}, {1 + radius(\phi) * sin(\phi)});
\draw[domain=-130:{atan(-1/3)-0.01}, variable=\phi, red, smooth, ultra thick] plot ({radius(\phi) * cos(\phi)}, {1 + radius(\phi) * sin(\phi)});
\end{tikzpicture}

ok wanted of modify this graph to be this
$y=−\sqrt{\dfrac{(x2+1}{2}}\textit{ (c) }−\infty<x<\infty$

https://mathhelpboards.com/threads/b-2-2-16-ivp-of-dfrac-x-x-2-1-4y-3-y-0-dfrac-1-sqrt-2.28981/

 

[NateD]

\begin{tikzpicture}[declare function = {radius(\phi)=sqrt(-2*(x^2+1)); },]\draw[->] (-3,0) -- (3.4,0);\draw[->] (0,-2) -- (0,4.2);\draw[domain=-130:130, variable=\phi, red, smooth, ultra thick] plot ({radius(\phi) * cos(\phi)}, {1 + radius(\phi) * sin(\phi)});\end{tikzpicture}