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Problem 62 Hard Difficulty

Where does the normal line to the parabola $ y = x^2 - 1 $ at the point (-1, 0) intersect the parabola a second time? Illustrate with a sketch.

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Video Transcript

Yeah, it's clear. So inhumane here. So we're finding where the normal line to the parappa below y equals X squared minus one. That negative one comma zero intersects the graph a second time. We're gonna first take the derivative and get two acts. And this gives us a slope of two. Which means our perpendicular slope is 1/2 which is our normal. So, are you normal? Up a M of end? We'll take the points, X I'm a X squared minus one and negative one comma zero. Get a square minus one minus zero. Over X minus. Negative one. We get excess ik X minus one. We're going to set them equal to each other for 1/2 is equal to X minus one. We get X is equal to three over two. You know why I value when we plug it in by over four. To get our normal line equation? We just put our X and why values in we get 1/2 X plus 1/2 the one we graft this. I look like this, our crapola. And then I lie. They touch each other, and right here we're talking about the intersection right here.