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we're ready for step two in our search for the elusive formula of how to compute a point exactly on a parabola to gain some intuition let's go back to the Interactive's that we use to kick this all off so here's my string art construction with a bunch of lines and now let me cycle through the lines one at a time highlighted here in magenta there's one of them here's another one here's another one and each of these magenta lines can be described by some fraction T that names that point on the line as I wiggle the magenta line back and forth notice that it continues to touch the parabola in exactly one place well if I can develop a formula for where that place is that's the formula I'm looking for we can see that even more clearly in this version of the interactive that you'll be using in a moment to solve a couple of exercises so in this version I can use this parameter T to name which string art line I'm talking about and notice that each of the string art lines touches the parabola in exactly one place in the next exercise you'll be asked to come up with a hypothesis for where that place is and the hypothesis as a hint has something to do with the ratios of these sub segments that are being created and we've color-coded those sub segments to give you an even more of a hint so see if you can figure out what that special relationship is