This question is about one of Descarte's machines and showing that it draws a parabola. See attached. Thank you This problem illustrates one of Descartes' machines (Fig.14.21). Here GL is a ruler pivoting at G. It is linked at Lwith a device CNKL that allows L to be moved alongAB, always keeping the line KN parallel to itself. Theintersection C of the two moving lines GL and KN de-termines a curve. To find the equation of the curve, beginby setting CB = y, BA = x, and the constants GA = a,KL =b, and NL = c. Then find BK, BL, and AL in termsof x, y, a, b, and c. Finally, use the similarity relation CB:BL = GA: AL to show that the equation isy? = cy - xy +ay – ac.Descartes stated, without proof, that this curve is a hyper-bola. Show that he was correct.BFIGURE 14.21Descartes' curve-drawing instrument

Given: GL is the ruler pivoting at G CNKL is the device that allows L to be moved along AB KN…

Answered: CB :BL= GA:AL to show that the cquation…

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CB :BL= GA:AL to show that the cquation is y? = cy - xy + ay – ac. Descartes stated, without proof, that this curve is a hyper- bola. Show that he was correct. FIGURE 14.21 Descartes' curve-drawing instrument