0

What is the locus of points $(s,t)$ equidistant from the convex side of parabola $y = x^2$?

Now, it is quite easy to determine s and t separately as functions of x, but can you define t as a function of s? Can it even be done?

When the question is applied to the concave side, something interesting happens.

Blue
  • 75,673
brogine
  • 1
  • 1
    I don't understand what you mean by "convex side" or "concave side". please explain. Also what do you mean by "equidistant from"? You state "quite easy to determine $s$ and $t$". If so, then please place this determination in your question. – Somos Jan 21 '21 at 18:58
  • 1
    Welcome to Math.SE! ... If you're posing a challenge whose answer you already know, say so explicitly in the body of the question (as comments are easily overlooked); the predominant assumption here is that a question is a request for help, so it's important to indicate when this isn't the case. If you are in fact seeking help, then please include the work you've done (eg, easily showing $s$ and $t$ separately as functions of $x$), so that people don't waste time duplicating your effort or explaining things you already understand. – Blue Jan 21 '21 at 18:59
  • If you need help, I made this desmos graph, it isn't much but I hope it will give you some idea – Some Guy Jan 21 '21 at 19:23
  • https://www.desmos.com/calculator/1yqxbmmlpt – Some Guy Jan 21 '21 at 19:23
  • This is better, use this https://www.desmos.com/calculator/xwgb3ict4i – Some Guy Jan 21 '21 at 19:36
  • @brogine Something like this : https://math.stackexchange.com/questions/61182/formula-for-curve-parallel-to-a-parabola ? – cosmo5 Jan 21 '21 at 20:15

0 Answers0