Some students try to use the concept of 0 gh og as gh

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Some students try to use the concept of 0 GH OG   as GH OG   . But this method is tedious and has higher chance of making calculation errors. It is good to offer the reason why | t | = t . Students should covert the position vector of H to coordinates of H . Thinking: | t | = t since t > 0
16 8 A curve C is defined parametrically by 2 2 , where x t y t t Points P and Q are the points on C where t = p and t = q respectively. (i) Find the equation of the chord PQ . [2] .
(ii) Show that pq = 1. (iii) Find d d y x in terms of t . (iv) Deduce the angle between the tangent to C at P and the tangent to C at Q . (v) The two tangents to C at P and Q intersect at the point N . Show that N lies on the line y = –1. [3] (vi) Find a cartesian equation of the curve traced by the mid-point of PQ as P and move along C . [3] [1] [1] [1] Q Solution Marker’s Comment q q : (i) p ) q )
17 “Deduce” means you would need to use the earlier results. (v) Equation of tangent at 2 2 , P p p 2 ( 2 ) Alternative Equation of tangent at = Equation of chord PQ when : , P p ) 1 is
18 9 The function f is defined by 1 f : , , 1, 1 ax x x x x and a is a positive constant. (i) Sketch the graph of f( ), y x indicating clearly the equations of the asymptotes and axial intercepts. Explain why the inverse of f exists. [3] (ii) Given that the point 1, 2 lies on the graph of 1 f ( ), y x find the value of a . [1] .
TJC H2 JC1 MYA 2021 9758/01