How can I find out that the curves included in the $y=c(2x+c)$ are orthogonal when $c$ is a random constant? I've tried defining $c$ with $x$ and $y$ but I failed.
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$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotMar 19 at 16:05
$\begingroup$ @Strawberry: The envelope is a zero radius circle at the origin. Please feel free to roll back if it was not a typo. Please mention the Clairaut's form ode $y=2cx+c^2$ has a solution as a set of tangents as context. $\endgroup$– NarasimhamMar 19 at 16:23
1$\begingroup$ One line has slope $2c$ and another has slope $2c'$. How will these possibly be orthogonal unless $4cc'=-1$? (And please rewrite your title.) $\endgroup$– Ted ShifrinMar 19 at 19:22
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