Answer Happy

Question 6. In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, consider joining the points (a,0) and (0,b) where a+b=1 and 0 <a,b<1. Page 2 of 3 A MTH1020 ASSIGNMENT 4 SEMESTER 1, 2022 1 We will show in this problem that all these straight lines are tangent to the curve with equation V1 + Vy=1 (with 0 < 1. x< 1). (a) Show that the line joining (6.0) and (0.5), where a + b = 1 and 0 < a, b < 1. has equation bray - ab (b) Show that if I andy are related by the equation Vi+y=1. then SI 正 EV le) Let (p.g) be a point on the curve IV - 1. Show that the tangent line to this curve at (p:) is cuation TV7+ vt - V17- (d) Explain why the linex considered in parts (a) and (c) are the same, ie the lines we originally drew in part are prochely the tangent lines to the curve Vi+v=1