Archimedean triangle in conic parabola: tangent method and size comparison

College entrance examination mathematics finale topic finale topic system explains column 219 lesson: college entrance examination mathematics conic curve study method guidance – parabola tangent method, line length comparison size problem.The position of a line and a parabola, the Archimedes triangle.So the first one, let’s figure out the range of slopes of line L.We can put it in point-slope form, where the line L is parallel to the parabola, and since there are two intersecting points, the discriminant is greater than zero, and then we can figure out the range of k, which is relatively easy.Second, let’s compare the size of PM and PN. What should we do then?We can figure out the coordinates of M and N, and for M we have to write the equation of the tangent line through A.We’ve talked a lot about this, but you can either rewrite it directly, or you can do it with a derivative, because it’s a function, so that’s the first step.We take the derivative, we get the slope of L1, and then using point-slope form, we write the equation of the tangent line, and we find the distance to PM.And now we have to make it clear that if we were to find PN, we would do the same thing.So what do we do with these two lengths?Of course we can use the difference method, we can also use the quotient method, in this case it is more convenient to use the quotient method, why?Think about it.And then using the treatment method of the asymmetric Weida theorem to do the homogeneous reduction, you will see.Ok, so that’s where we’re going, and we’re going to move on to the Archimedes triangle next time.Learning system please check column: for details, please click on, look at the first class high school mathematics and general method: kill conic (analytic geometry: elliptic hyperbolic parabolic) 6 d coordinate system 399 yuan to buy a column more content: the college entrance examination mathematics research method instruction: using derivative function of the tangent of the two kinds of questions, please collect applicable grade three!If you want to know more about it, please pay attention to the six-dimensional coordinate system

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