# How can I find out if a curve is orthogonal using differential equations

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.

• 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.
– Community Bot
Mar 19 at 16:05
• @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. Mar 19 at 16:23
• One line has slope $2c$ and another has slope $2c'$. How will these possibly be orthogonal unless $4cc'=-1$? (And please rewrite your title.) Mar 19 at 19:22